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Rayica User Guide

1. We can instead combine the lens and mirror with Resonate to create a self contained non sequential aggregate of the surfaces present In 24 lensMirror Resonate Move PlanoConvexLens 100 50 10 50 Move Mirror 50 5 75 Out 24 Resonate Move PlanoConvexLens 100 50 10 50 Move Mirror 50 5 75 1994 2005 Optica Software All rights reserved 52 Rayica User Guide Although the lens and mirror are still identified in the output as independent elements in fact Resonate has melded their information into a single Component object This can be observed if we examine the Head of the lensMirror variable assignment In 9 Head lensMirror Out 9J Component This indicates that the lens and mirror surfaces have been joined together under a single Component roof The rays now correctly trace through this new arrangement In 99 AnalyzeSystem LineOfRays 45 lensMirror Boundary 100 PlotType gt TopView 1994 2005 Optica Software All rights reserved Rayica User Guide 53 Resonate works independently from whether AnalyzeSystem or TurboP1ot is used for tracing Here the same system is traced with TurboPlot In 100 TurboPlot LineOfRays 45 lensMirror Boundary 100 PlotType gt TopView You can learn more about Resonate and non sequential tracing in Section 3 3 of the Principles of Rayica G
2. 500 0 0006963 460 0 0010454 436 0 0010454 420 0 0012203 405 0 0012203 400 0 0015705 390 0 0019215 380 0 0035096 370 0 0045764 365 0 0054705 350 0 0126068 334 0 0454037 320 0 182373 310 0 461961 300 0 609152 KnoopHardness gt 610 MassDensity gt 2 51 OpticaFunction gt SellmeierFunction OpticalMedium gt BK7 PhosphateResistance gt 2 3 PoissonRatio gt 0 206 SpecificHeat gt 8 58x10 SpectralIndex gt mone 2325 4 1 48921 none 1970 1 1 49495 none 1529 6 1 50091 none 1060 1 50669 t 1014 1 50731 s 852 1 1 5098 r 706 5 1 51289 C 656 3 1 51432 Cprime 643 8 1 51472 HeNe 632 8 1 51509 D 589 3 1 51673 d 587 6 1 5168 e 546 1 1 51872 F 486 1 1 52238 Fprime 480 1 52283 g 435 8 1 52668 h 404 7 1 53024 i 365 1 53627 none 334 1 1 54272 none 312 6 1 54862 StainResistance gt 0 TemperatureCoefficientIndex gt 1 86x10 1 31x10 1 37x10 4 34x107 6 27x10 7 0 17 ThermalConductivity gt 1114 ThermalExpansion gt 30 70 7 1x10 20 300 8 3x10 TransformationTemperature gt 557 ViscousTemperaturel gt 557 ViscousTemperature2 gt 719 WaveLengthRange gt 0 3 2 325 In this entry all of these listed rules describe some aspect of the BK7 glass material Rayica s database is made up of thou sands of entries that are forma
3. 0 001 CosineCompensation gt True SequentialRead gt Automatic InterpolatingFunction gt False InterpolationOrder gt 1 SampleFactor gt 2 RecenterData gt False RunningCommentary gt False Here we can see that FindIntensity uses a number of options that we have not encountered before The most significant of these are listed below Out 12 TableForm IntensitySetting Print SequentialRead ReportedSurfaces IntensityScale Show KernelScale SmoothKernelRange Plot2D SmoothKernelSize Options that help characterize FindIntensity While some of these options will be considered further in this section others will be left to discussion elsewhere In addition to showing information as a three dimensional plot the Plot2D option in FindIntensity has several other settings Its settings are shown below False or Ful13D gives the full three dimensional rendering of the intensity profile True or SideView gives a two dimensional cross section rendering at the x z plane of the intensity profile FrontView gives a two dimensional cross section rendering at the y z plane of the intensity profile ContourPlot gives a contour plot of the intensity profile Settings of Plot2D Next we shall plot the same FindIntensity calculation with its default plot setting Plot2D gt ContourPlot This time we call FindIntensity with the previous results stored in intensityresult This saves us from having to rerun the ray trace
4. AnalyzeSystem system options is used to trace rays through optical components and render the results for illustration purposes This is also called DrawSystem PropagateSystem system options is used by AnalyzeSystem to trace rays through optical components This method is much slower than TurboTrace TurboTrace optics options produces an accelerated ray trace of a system of light sources and optical elements TurboP1lot system options works with TurboTrace to perform accelerated ray tracing and rendering of a system of light sources and optical elements ShowSystem system options takes a system of rays and or components and generates a graphical display of the system ShowSystem works with AnalyzeSystem and TurboP1lot results ReadRays results rayparameters selectionproperties takes ray traced results from AnalyzeSysten TurboPlot TurboTrace and returns a list of values for the rayparameters and selectionproperties given OptimizeSystem system options optimizes the performance of an optical system for a specified set of symbolic input parameters FindFocus objectset options determines the minimum spot size for a locus of rays at the last reported surface in the system and plots the results FindSpotSize objectset options determines the spot size for a locus of rays at the last reported surface in the system and plots the results FindIntensity system options calculates the intensity function for each optical surface
5. False IntersectionNumber gt IntersectionNumber IntrinsicMedium gt Air NewAuthorizedOptions gt NewAuthorizedOptions OffAxis gt OffAxis OpticalLength gt 0 OpticalMedium gt Automatic Polarization gt 0 1 0 RayEnd gt 0 0 0 RayLabelPositions gt 0 0 0 RayLabels gt RayLength gt 0 RayLineRGB gt Automatic RayLineStyle gt RayLineThickness gt 0 5 RayPointRGB gt 0 0 0 RayPointSize gt 2 RayPointStyle gt RaySourceNumber gt RaySourceNumber RayStart gt 0 0 0 RayTilt gt 1 0 0 RefractiveIndex gt Automatic RotationMatrix gt 1 0 0 0 1 0 0 0 1 SourceID gt Automatic SourceTransformation gt 0 0 0 1 0 0 0 1 0 0 0 1 SurfaceBoundary gt SurfaceBoundary SurfaceCoordinates gt SurfaceCoordinates SurfaceID gt SurfaceID SurfaceIncrement gt 1 SurfaceNormalMatrix gt SurfaceNormalMatrix SurfaceNumber gt SurfaceNumber SymbolicWaveLength gt SymbolicWaveLength Temperature gt 20 Tension gt 101300 0 0 0 101300 0 0 O 101300 UnconfinedIncrement gt 1 UnconfinedPath gt UnconfinedPath UnconfinedPosition gt UnconfinedPosition WaveFrontID gt Automatic WaveLength gt 0 532 Options Ray applies to all of Rayica s light sources since it determines what default values will be used by the rays at the start of the trace In some cases a parameter many not h
6. the following discussion is simply provided to help the user gain further insight into how Rayica s handles the ray trace information For the most part these mechanisms are hidden away from the Rayica user If you are learning about Rayica for the very first time you can skip this section without penalty At the start of a ray trace both PropagateSystem and TurboTrace use the CreateRays function to convert Source objects into either Ray or TurboRay objects This initializes the ray information for the trace CreateRays Source options is used by PropagateSystem and TurboTrace to generate either Ray objects or a TurboRays object that represents a set of rays for the given light source Ray rules contains rules that is used by PropagateSystem to characterize a single ray segment of light between two optical surfaces TurboRays raysegment raysegment2 gives a collection of ray segment parameters for use with TurboTrace The Ray and TurboRays objects offer two parallel ways of storing the same information about rays In particular the Ray object is used by PropagateSystem to hold ray information while the TurboRays object is used instead by TurboTrace As an example we will use the WedgeOfRays function to generate three rays First we will assign the WedgeOfRays result into a variable called wedgeofrays In 20 wedgeofrays WedgeOfRays 10 Out 20 WedgeOfRays 10 With InputForm we can see that like Single
7. 0 RefractiveIndex gt 1 0002694514570802 RotationMatrix gt 0 9961946980917455 0 08715574274765817 0 0 08715574274765817 0 9961946980917455 0 0 0 1 SourceID gt 2118 SourceTransformation gt 0 0 0 1 0 O0 O0 le 0 O O 1 WaveFrontID gt 2118 0 Here each Ray object represents a different ray segment When TurboTrace is used for ray tracing it works instead with a TurboRays object The OutputType option is used with CreateRays to determine whether CreateRays generates a Ray object or a TurboRays object from the Source information By default createRays creates Ray objects However when TurboTrace calls CreateRays it passes OutputType gt TurboRays to obtain a TurboRays object Next we apply CreateRays to wedgeofrays for a second time with OutputType gt TurboRays 1994 2005 Optica Software All rights reserved 14 Rayica User Guide In 21 CreateRays wedgeofrays OutputType gt TurboRays InputForm Out 21 InputForm TurboRays 0 0 O0 O O O 0 9961946980917455 0 08715574274765817 0 0 08715574274765817 0 9961946980917455 0 0 0 1 0 532 100 0 33333333333333337 0 1 0002694514570802 0 0 O O O O 0 2118 2118 1 3 1 O 1 O O O Dag O 0 O O O O O 1 0 O O le O O Ov 1 0 532 100 0 33333333333333337 0 1 0002694514570802 0 0 O O O 0 O 2118
8. 000 CenterThickness gt 16 2 CompanyName gt JML ComponentBoundary gt 50 ComponentLabel gt PlanoConvexLens ComponentMedium gt Quartz Date gt 1999 4 18 DesignWaveLength gt 587 6 EdgeThickness gt 2 6 FileName gt JML m FNumber gt 1 3 FocalLength gt 65 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 29 8 SurfaceBoundary gt 50 50 SurfaceSeparation gt 16 2 V1H1 gt 0 V2H2 gt 11 1 In this particular case Rayica has isolated a single database entry that perfectly matches the desired parameters At this point we can call DataToRayica to create the chosen component in Rayica In 25 lens DataToRayica PlanoConvexLens ComponentBoundary gt 50 FocalLength gt 65 ShowSystem lens Out 25 J PlanoConvexLens 65 50 16 2 ComponentMedium gt Quartz DesignWaveLength gt 0 5876 In other cases when more than one match exists Rayica will recover the closest matches that fit within a certain tolerance In this next example Rayica finds six close candidates 1994 2005 Optica Software All rights reserved 58 Rayica User Guide In 74 SearchData PlanoConvexLens ComponentBoundary gt 50 FocalLength gt 75 Out 74 CatalogNumber gt LOF066 CenterThickness gt 13 8 CompanyName gt MellesGriot ComponentBoundary gt 50 ComponentLabel gt OpticalQualityPlanoConvex ComponentMedium gt FusedSilica Date gt 1999 4 18 DesignRefractiveIn
9. 2118 2 3 2 0 1 O0 O O 1 O 0 O0 O O O O 0 9961946980917455 0 08715574274765817 0 0 08715574274765817 0 9961946980917455 0 0 O 1 0 532 100 0 33333333333333337 0 1 0002694514570802 0 Osy Osy O Osy O O 2118 2118 3 3 3 0 1 0 Osy Osp 1 O This time only a single TurboRays object is produced that contains three sets of numbers In this case each set of numbers represents a different ray segment From this we can see that TurboRays is much more efficient at holding information than Ray objects This is gives TurboTrace the ability to work with very large ray data sets and consume less memory How ever the Ray object is much more flexible at holding different sorts of optical parameters such as user defined parameters This in turn gives PropagateSystem added flexibility over TurboTrace for tracing customized information In general however the user of Rayica will never work directly with Ray and TurboRays objects and these conversions happen transparently In the next section we will learn about Options Ray Options Ray is used by CreateRays to fill in any essential ray parameters missing from the specified Source object during its ray creation How Rayica manages default light source settings In Rayica as well as Mathematica most built in functions have a way to pass default settings about certain parameters This relieves the user from always having to sp
10. FNumber gt 1 5 FocalLength gt 75 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 34 38 SurfaceBoundary gt 50 50 SurfaceSeparation gt 12 7 V1H1 gt 0 V2H2 gt 8 7 BackFocalLength gt 67 5 CatalogFocalLength gt 75 CatalogNumber gt CPX10195 100 CenterThickness gt 11 4 CompanyName gt JML ComponentBoundary gt 50 ComponentLabel gt PlanoConvexLens ComponentMedium gt BK7 Date gt 1999 4 18 DesignWaveLength gt 632 8 EdgeThickness gt 2 2 FileName gt JML m FNumber gt 1 5 FocalLength gt 75 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 38 63 SurfaceBoundary gt 50 50 SurfaceSeparation gt 11 4 V1H1 gt 0 V2H2 gt 7 5 CatalogNumber gt 43 0462 CenterThickness gt 11 6 CompanyName gt Coherent Ealing ComponentBoundary gt 50 ComponentLabel gt 43 0462 PLANO CONVEX PlanoConvexLens ComponentMedium gt BK7 Date gt 1999 4 18 DesignRefractiveIndex gt 1 5168 DesignWaveLength gt 0 5876 EntrancePupilDiameter gt 45 FileName gt CoherentEaling m FocalLength gt 75 0003 GlassCatalogs gt SCHOTT MISC INFRARED OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 38 76 StopPosition gt 1 SurfaceBoundary gt 50 50 SurfaceCurvature gt 0 0257998 0 SurfaceLabel gt SphericalShape SphericalShape SurfaceSeparation gt 11 6 With so many reported entries the SearchData results can get to
11. The ShowSystem Function After making the ray trace with AnalyzeSystem you can redisplay the results more quickly with ShowSystem Here we use the previous AnalyzeSystem output stored in the trace variable as the input to ShowSystem We will suppress the printed output text by including a semicolon at the end of the input expression In 4 ShowSystem trace PlotType gt TopView Axes gt True MinimumArrowLength gt 0 30 20 10 50 NS ee Here the rendered result shows three arrows that correspond with the three ray segments previously calculated by Analyze System during the trace ShowSystem and AnalyzeSystem both use the same options for graphical rendering Although there are a great many options available for graphical rendering some of most important options are listed in the following table 1994 2005 Optica Software All rights reserved Rayica User Guide 23 AppendGraphics PrependGraphics Axes RayChoice ColorView ShowArrows CreateStereoView ShowClones DefaultStyle ShowComponents GraphicDesign ShowLabels MinimumArrowLength ShowRange PlotType ShowText Important rendering options In most instances only one or two rendering options will be needed to display any particular result In the previous ShowSys tem example we used three different rendering options PlotType Axes and MinimumArrowLength Of these three options however only the PlotType option is
12. TopView RunningCommentary gt TurboTrace ShowArrows gt All1 System traced in 11 5 seconds with 504 ray segments getting reported af 00o 990900 ee rp 1994 2005 Optica Software All rights reserved 38 Rayica User Guide In this example Rayica has modelled a system of 882 optical surfaces By using CreateClones this result is 1200 times faster than the same calculation would have been with AnalyzeSystem and 66 times faster than TurboPlot alone In addition in this example CreateClones has consumed only 1 400 of the memory that would otherwise have been required to describe the same optical system The performance of CreateClones improves even further as its number of repetitive elements is increased In some cases CreateClones can reach efficiencies that are tens of thousands times better than otherwise possible You can learn more about CreateClones in Chapter 7 of the Principles of Rayica Guide In addition to the CreateClones option this example has used three other new options These are defined below ShowClones gt True False is an option that denotes whether the phantom clones of optical components are rendered ShowArrows gt True False Al1 maxnumber is an option that switches between arrow and simple line rendering of rays RunningCommentary gt True False Al1 TurboTrace ComponentFoundation is an option of PropagateSystem TurboTrace and other Rayica functions that controls reporting of the cal
13. True TransferDeflectionFunction gt False Boundary 150 PlotType gt TopView 1994 2005 Optica Software All rights reserved Rayica User Guide 63 21 What s Missing This section provides a road map of the features missing from either the User Guide discussion or the basic Rayica package as a whole The User Guide discussion has been designed to help the novice user become familiar with the basic features in Rayica In some instances in order to avoid overwhelming the user with the more specialized capabilities of Rayica some topics have been omitted from this discussion In other instances certain aspects of optical modelling have not been included in the basic Rayica package but have instead been incorporated into extensions of Rayica Finally there can be occasions when a feature is not yet built into the Rayica system This section will help you to determine the status of any particular feature not discussed previously in the User Guide discussion If you should discover that a desired feature is missing from Rayica then please contact optica support and let us know about it We will try our best to help you to find an appropriate solution to your modelling problem In addition Optica Software offers a consulting service for custom solutions in Rayica Features not discussed here The User Guide discussion does not discuss every feature present in Rayica In particular there ha
14. and components in a list whose order describes the order of the light propagation through the optical components Coordinates In Rayica the X axis runs in the horizontal direction parallel to the computer screen and is the default optical axis for optical systems components within systems and surfaces within components The Z axis encompasses the vertical direction and the Y axis is right handed with respect to the X and Z directions Within an optical system components and rays are located using the system s world coordinate system Each surface within a component has its own local coordinate system and carries a three dimensional rotation matrix plus a three dimensional translation vector to transform a point or ray from the world coordinate system into the surface s local coordinate system and back This world to surface transform matrix plus vector is derived by combining the world to component and component to surface transforms during component initialization Modeling a light source Next we will take a closer look at light source functions Rayica has a built in series of functions that model different patterns of ray light sources Here is a list of the most common built in light source functions 1994 2005 Optica Software All rights reserved 10 Rayica User Guide SingleRay options constructs a single ray of light with its starting position at the origin and is directed down the positive x axis CircleO
15. and intensity calibration We will use Print gt False to switch off the printed messages Show gt False can be used to switch off the graphical rendering 1994 2005 Optica Software All rights reserved Rayica User Guide 43 In 5 FindIntensity intensityresult Print gt False Surface Intensity FindFocus In the previous example we examined the intensity at a single surface However if multiple surfaces are reported FindIn tensity can measure the energy losses in the system that occurs between the first reported surface and every subsequent reported surface We will see this in the next example Here we use an ApertureStop as a pupil that restricts the transmit ted light through a lens In addition we will use FindIntensity to calculate the point spread function of the optical system by placing one of the reported surfaces at the lens focal point Before running FindIntensity we will first use TurboPlot to show a ray trace of our intended system In 43 trace TurboPlot GaussianBeam 5 05 NumberOfRays gt 12 FullForm gt True Move ApertureStop 50 15 49 Move PlanoConvexLens 100 50 10 50 Move Screen 50 225 PlotType gt Full3D 1994 2005 Optica Software All rights reserved 44 Rayica User Guide In order to measure the point spread function of the lens system you first need to determine the focal point of the system You can use the FindFocus function for this He
16. be confusing In order to clarify the important information you can use ReadData instead of SearchData in order to view isolated parameters from the data base search We will now use ReadData with the same parameter search as before In 75 ReadData ComponentBoundary FocalLength CatalogNumber PlanoConvexLens ComponentBoundary gt 50 FocalLength gt 75 Out 75 DisplayForm ComponentBoundary FocalLength CatalogNumber 50 75 0089 LOF066 50 75 0089 LOP005 50 75 0027 PCX45246 50 75 FPX11730 000 50 75 CPX10195 100 50 75 0003 43 0462 1994 2005 Optica Software All rights reserved Rayica User Guide 59 From this information we can see that two items actually match up perfectly with the desired parameters We can now place the CatalogNumber from our favorite result in DataToRayica to define an actual lens in Rayica In 27 lens DataToRayica FPX11730 000 Out 27J PlanoConvexLens 75 50 12 7 ComponentMedium gt Quartz DesignWaveLength gt 0 5876 In some instances there may not be any suitable match with a database entry In such cases an empty list is returned In 39 SearchData nothing Out 39J In 38 DataToRayica nothing Out 38j You can learn more about Rayica s database system in Chapter 5 20 The TransferTraits Function One of the most recent additions to Rayica s constellation of high level functions is TransferTraits TransferTraits
17. gt Automatic RayPointRGB gt 0 0 0 RaySourceNumber gt 1 3 1 0 RayStart gt 0 0 0 RayTilt gt 0 9961946980917455 0 08715574274765817 0 RefractiveIndex gt 1 0002694514570802 RotationMatrix gt 0 9961946980917455 0 08715574274765817 0 0 08715574274765817 0 9961946980917455 0 0 0 1 SourceID gt 2118 SourceTransformation gt 0 0 0 1 0 O0 O0 le 0 O0 O 1 WaveFrontID gt 2118 0 Ray Intensity gt 100 IntensityScale gt 1 OpticalMedium gt Air Polarization gt 0 1 0 RayEnd gt 0 0 0 RayLabelPositions gt 0 0 0 RayLength gt 0 RayLineRGB gt Automatic RayPointRGB gt 0 0 0 RaySourceNumber gt 2 3 2 0 RayStart gt 0 0 0 RayTilt gt 1 0 0 RefractiveIndex gt 1 0002694514570802 RotationMatrix gt 1 0 0 0 1 0 0 0 1 SourceID gt 2118 SourceTransformation gt 0 0 0 1 0 0 0 1 0 0 O 1 WaveFrontID gt 2118 O Ray Intensity gt 100 IntensityScale gt 1 OpticalMedium gt Air Polarization gt tots Ier Ody RayEnd gt 0 0 0 RayLabelPositions gt 0 0 0 RayLength gt 0 RayLineRGB gt Automatic RayPointRGB gt 0 0 0 RaySourceNumber gt 3 3 3 0 RayStart gt 0 0 0 RayTilt gt 0 9961946980917455 0 08715574274765817
18. level and converts the database information into a function ing optical component or material model for use with Rayica DataToRayica however usually retrieves only a single item from the database listing Very often therefore you will want to use SearchData and ReadData first to survey which of the neighboring database items also have a close match to your specifications in order to make the best choice for DataToRayica 1994 2005 Optica Software All rights reserved 54 Rayica User Guide In essence Rayica s database contains an array of information that is stored in the form of lists of rules Each rule describes a particular data attribute given by parametername gt value As an example the following database entry describes the BK7 optical glass In 10 SearchData OpticalMedium gt BK7 Out 10J AcidResistance gt 1 AlkaliResistance gt 2 BubbleClass gt 0 ClimaticResistance gt 2 ColorCode gt 330 300 CompanyName gt Schott ComponentLabel gt glass Date gt 1999 4 18 Dispersion gt 1 5168 64 17 63 96 0 0 008054 0 00811 ElasticModulus gt 82000 FileName gt Schott m GlassCodeNumber gt 517642 IndexCoefficients gt 1 03961 0 231792 1 01047 0 0060007 0 0200179 103 561 InternalTransmittance gt 2325 0 0976501 1960 0 0282324 1530 0 0026255 1060 0 0003478 700 0 0003478 660 0 0005219 620 0 0005219 580 0 0006963 546 0 0006963
19. need to do is click on an item in the list to have its description displayed In this Guide we will explore many of these different functions in some detail In some instances this discussion serves as the primary reference for the subject matter In other instances however the subject is discussed in more detail elsewhere Next we will learn how to create models of optical components and light sources 2 Modeling Optical Components and Light Sources Rayica has its own language for describing optical systems In general Rayica considers an optical system to be a collection of light sources and optical components There are many different types of components and light sources in Rayica and each type is specified by a particular function For example a parallel light sheet is modeled by the LineOfRays function while a mirror is modeled by the Mirror function After evaluation these functions generate one of two special data structures that carry the optical properties In particular all component functions create a Component object while all light source functions create a Source object In this section you will learn how to use component functions and light source functions to model optical components and light sources Later on you will learn how to define an optical system by listing together a combina tion of light sources and optical components In particular you will see that you can specify an optical system by placing your light sources
20. of its use In addition to ones listed here you can build your own custom component functions as well as download new functions from the Optica Software web site www opticasoftware com One of the most frequently used component functions is PlanoCon vexLens PlanoConvexLens focallength aperture thickness options refers to a lens with a planar surface on one side and a convex spherical surface on the other side Here is how you evaluate the PlanoConvexLens function 1994 2005 Optica Software All rights reserved Rayica User Guide 17 In 18 PlanoConvexLens 100 50 10 Out 18J PlanoConvexLens 100 50 10 In the same fashion that ray source functions create Source objects every component function creates a Component object In this PlanoConvexLens example hidden behind the PlanoConvexLens 100 50 10 output returned to the screen is a very large expression that is encapsulated with the Component head It contains detailed information to describe a plano con vex lens having a focal length of 100 millimeters a circular aperture 50 millimeters in diameter and a lens center thickness of 10 millimeters Instead of showing this entire expression Rayica always hides the contents of Component by outputting back to the screen a description of how the component was generated Here again Rayica indicates a valid entry by returning the text in a different color from black As with light source functions and
21. offers the user a powerful way to quickly customize a built in optical component by transferring some of the characteristics from a second component TransferTraits donor component recipient component surfacenumbers opts is a function that transfers the surface traits of a donor component surface into the surfaces specified by surfacenumbers of a recipient component As an example lets change the behavior of a plano convex lens In 10 lens Move PlanoConvexLens 100 50 10 50 AnalyzeSysten LineOfRays 45 NumberOfRays gt 11 lens Boundary 150 PlotType gt TopView We can now use TransferTraits add a reflective surface onto the first surface of the lens by transferring these traits from a simple mirror 1994 2005 Optica Software All rights reserved 60 Rayica User Guide In 12 mirror Mirror 50 AnalyzeSysten LineOfRays 45 NumberOfRays gt 11 TransferTraits mirror lens 1 Boundary 150 PlotType gt TopView We can instead add the reflective behavior of a mirror onto the second surface of the lens by using 2 instead of 1 for the surface number specification In 11 AnalyzeSystem LineOfRays 45 NumberOfRays gt 11 TransferTraits mirror lens 2 Boundary 150 PlotType gt TopView Furthermore by rotating the mirror slightly first TransferTraits will transfer not
22. that gets reported from the ray trace of the system ModulationTransferFunction intensitydata options calculates the modulation and phase transfer functions of an optical system for a given object source input Resonate istofcomponents objectname options is a generic building block that causes a ray to be nonsequentially traced within all of the surfaces defined by listofcomponents TransferTraits donor component recipient component surfacenumbers opts is a function that transfers the surface traits of a donor component surface into the surfaces specified by surfacenumbers of a recipient component Rayica s most important high level functions In various ways these high level functions assist the user in conducting the ray trace and interpreting the traced results At the heart of every high level function in Rayica is the ray trace calculation For this Rayica offers two parallel ways to trace rays through a system of optical elements in three dimensional space using either PropagateSystem or TurboTrace In many cases however the ray trace needs to be accompanied by a graphical rendering of the traced system In such instances either AnalyzeSystem or TurboPlot is called instead of PropagateSystem or TurboTrace In other instances ShowSys tem is used to render isolated components or to rerender the results after the initial trace has taken place ReadRays is used to extract numerical information from the traces previ
23. the Source object since the Component object is automatically created by the built in component functions the user of Rayica will never need to worry about the details of this Component object In fact unless you use InputForm as demonstrated previously with the Source object the contents of the Component object are always hidden Nevertheless it is helpful to understand what happens when you evaluate a component function As with light sources you can use these generated Component objects immediately after creating them for doing ray tracing and rendering or you can assign them to a variable for future work While focallength aperture and thickness are all parame ters given explicitly to the PlanoConvexLens function other implicit parameters such as the type of refractive material are kept as options of PlanoConvexLens You can use Options PlanoConvexLens to access the default options of Plano ConvexLens In 30 Options PlanoConvexLens Out 30J Labels gt L LabelPositions gt Automatic ComponentDescription gt Automatic ComponentMedium gt BK7 Temperature gt Temperature Tension gt Tension Transmittance gt Transmittance Reflectance gt Reflectance GraphicDesign gt Automatic CurvatureDirection gt Front DesignWaveLength gt 0 5461 OffAxis gt 0 0 SwitchDirectionOnReflection gt False Resonate gt True Automatic gt SurfaceRendering gt Empty EdgeRendering gt Mesh CrossRendering gt Fill T
24. the screen surface In 31 ShowSystem screensystem PlotType gt Surface RayChoice gt ComponentNumber gt 3 1994 2005 Optica Software All rights reserved 30 Rayica User Guide 11 The ShowRange Option Another useful option is ShowRange You can use ShowRange to zoom in on a particular portion of the system ShowRange gt values uses ComponentNumber values to select the components and ray segments displayed ShowRange can take either the value A11 or a list of the ComponentNumber values Here we examine the ray segments connected with the cylindrical lens In 63 ShowSystem screensystem ShowRange gt 2 ShowRange works differently from RayChoice because ShowRange displays selected components associated with the selected ray segments In addition ShowRange only works with ComponentNumber values whereas RayChoice works with many different selection parameters See Section 6 4 in the Principles of Rayica Guide for more discussion about ShowRange 12 The ReadRays Function It is often desirable to get specific numeric values for a selected set of parameters from the ray trace This can be accom plished with ReadRays ReadRays results rayparameters selectionproperties takes ray traced results from AnalyzeSystem PropagateSystem and returns a list of values for rayparameters and selectionproperties given Here we use ReadRays to examine the optical path length of ray
25. to be the optical axis This means that by default all of Rayica s built in light source functions automatically direct their rays along the positive x axis In this example the SingleRay function has generated a ray that is exactly co linear with the x axis In other more complex light source functions only the chief ray is precisely co linear with the x axis Of course you can always choose a different optical axis by re aligning the light source and optics with a positioning directive such as Move Working with the ray trace data After calculating and rendering the ray trace AnalyzeSystem passes back a data object that holds the ray trace information You can use this returned information to make further plots or exact numeric information about the generated ray trace In general depending on whether AnalyzeSystem or TurboPlot was used the final ray trace data is held in either an Opti calSystem object as in this case or a TurboSystem object with TurboPlot However as discussed before with Compo nent and Source the information held in these returned objects are always hidden from the user Rather than directly viewing these objects you will normally examine the ray trace results with one of Rayica s ray trace diagnostic functions These are listed below 1994 2005 Optica Software All rights reserved 22 Rayica User Guide ShowSystem system options takes a system of rays and or components and generates a graphical dis
26. you acquired this product in the United States this Agreement is governed by the laws of the State of Illinois Any dispute arising out of or in connection with this Agreement shall be adjudicated exclusively in the state or federal courts of the State of Illinois and all parties consent to personal jurisdiction and venue therein Should you have any questions concerning this Agreement or if you desire to contact iCyt for any reason please contact our website at http www opticasoftware com 8 LIMITED WARRANTY iCyt warrants the media on which any SOFTWARE PRODUCT is provided to be free from defects in materials and workmanship for ninety 90 days after delivery Defective media may be returned for replacement without charge during the ninety 90 day warranty period unless the media have been damaged by accident or misuse iCyt warrants for ninety 90 days after purchase that any unaltered SOFTWARE PRODUCT will substantially conform to the documentation that accompanies it iCyt expressly reserves the right to provide the documenta tion on the same media as the Updates Any implied warranties are limited to the duration of the express warranties stated in this Section 8 iCyt does not warrant that a operation of SOFTWARE PRODUCT shall be uninterrupted or error free b that functions contained in the SOFTWARE PRODUCT shall operate in combinations which may be selected for use by Licensee or meet Licensee s requirements or c tha
27. 1 lt gt RayBoundary gt 0 0692861 0 0692861 SmoothKernelSize gt 0 00135192 SurfaceNumber gt 1 WaveFrontID gt 1 This example demonstrates one of the great pitfalls in using a two dimensional result to model a three dimensional system In particular it is a strong temptation to assume that one can use the results from a two dimensional ray trace to gauge the performance of a three dimensional system Unfortunately this can be an erroneous assumption As illustrated by this example such intensity calculations can be very different from a three dimensional ray trace This is particularly evident at the focal plane in this example where both the point spread function and modulation transfer function looks very different from the previous three dimensional example This is because the energy density from the three dimensional trace through a radially symmetric lens system is much more concentrated along optical axis This last result actually depicts the behavior of a cylindrical lens system better than a plano convex lens in three dimensions However because the ray density is far greater in this recent example it has a much better spatial resolution than the previous example and quite accurately depicts the geometric light flux behavior of the two dimensional system 18 The Resonate Function Resonate is used to create non sequential behavior between formerly distinct optical elements Resonate is routinely used by many built
28. 274 155 243 155 232 155 231 155 232 155 232 155 232 155 231 155 232 155 243 155 274 Since ReadRays and ReadTurboRays both work with TurboTrace and TurboPlot it can be easiest to simply use Read Rays all of the time You can learn more about TurboTrace TurboPlot OptimizeSystem and ReadTurboRays in Section 3 6 of the Principles of Rayica Guide 17 Energy Calculations with Findintensity In addition to optimization Rayica can also help you determine the light intensity profile at specified optical surfaces and to measure the transmitted energy through the optical system This is accomplished with the FindIntensity function FindIntensity system options calculates the intensity function for each optical surface that gets reported from the ray trace of the system For its input FindIntensity works best with either an untraced raw optical system or a previously calculated result by FindIntensity However when required FindIntensity can also work with externally generated trace results FindIn tensity works equally well for surfaces that either are close to a focal plane or far from any focus If a light sheet source is used ie WedgeOfRays or LineOfRays then a one dimensional intensity function is automatically calculated by FindIn tensity If a volume filling source is used ie PointOfRays or GridOfRays then the intensity calculations are automati 1994 2005 Optica Software All rights reserved Rayic
29. Basic Commands section of this booklet Options are assigned to Rayica elements using what is known as a rule gt in Mathematica What this means is that you select an option or options to assign a value like Plot Type in the following example and then assign it a new value using the rule arrow In 17 TurboPlot tracedresult PlotType gt TopView Out 17 traced system If you are unsure of what new values can be assigned to an option you can use the command and the option s name to determine what values can be assigned to that option In 18 PlotType PlotType is an option of DrawSystem AnalyzeSystem TurboPlot and ShowSystem that designates the display form of the graphics rendering PlotType takes TopView FrontView SideView Full3D RealTime3D Off Surface and ShadowProject as values A list of one or two points specify a direction and center to project the graphics The points can be specified as rules RaySelect gt sel ComponentSelect gt sel and SurfaceSelect gt sel with sel being a list of selection properties passed to the designated functions See also CreateStereoView and ProjectGraphics3D 1994 2005 Optica Software All rights reserved 8 Rayica User Guide Rayica s high level functions Rayica has a number of functions available for high level calculations Some but not all of these functions are shown in the following table
30. FullForm gt True in the GaussianBeanm there have been in fact 647 4096 rays created This was the result of FullForm gt True If FullForm gt False has been used instead then only 64 rays would have been generated in total In general you are free to choose the number of rays to be traced with FindIntensity Bear in mind however that there needs to be a sufficient number of ray samples to make the FindInten sity result meaningful As a rule of thumb NumberOfRays gt 64 is the minimum value required for reasonable full sur face calculations to produce 4096 rays and NumberOfRays gt 256 is the minimum required for light sheet ray traces to produce 256 rays 1994 2005 Optica Software All rights reserved 42 Rayica User Guide You can use Options FindIntensity to observe its default option settings In 3 Options FindIntensity Out 3J KernelScale gt Relative SmoothKernelSize gt 6 SmoothKernelRange gt 3 IntensitySetting gt Automatic Energy gt Automatic IntensityScale gt 1 Print gt True Show gt True ReportedSurfaces gt Last SequentialTrace gt False GenerationLimit gt 200 PlotRange gt All PlotDomain gt Automatic PlotPoints gt 40 Plot2D gt ContourPlot ContourLines gt False Contours gt 50 Full3D gt Automatic ColorFunction gt Hue 0 65 10 65 1 10 9 0 1 amp FilterTrace gt True ScoutTrace gt Automatic ScoutRays gt Automatic ThresholdIntensity gt
31. Mathematica does not yet have a simple built in facility to generate stand alone Java or C code Once available this will enable high speed ray trace capabilities that are on par with every other optical design package on the market In addition Mathematica is still missing an interactive graphical user interface capability However once such features do become available in Mathematica we have already prepared Rayica to take advantage of them In the near future it is likely that Rayica and Wavica will be packaged together with a custom Mathematica engine to permit a single integrated optical design product that has wider appeal to non Mathematica users 22 Backward Compatibility Issues The new Rayica system has been rebuilt from the ground up As a consequence users of the original Optica will notice some important changes in the basic functional behavior of Rayica such as the use of Source objects to model light sources Such changes have resulted in many important new capabilities for Rayica While many of the changes in functional behavior have already been discussed in the User Guide presentation there have also been some important changes made to the input formats of certain functions in Rayica that have not been covered In this section we will examine some of these input format changes that may affect legacy code from Optica version 1 In general such format changes have been made to simplify the usability of the affected functions Per
32. Ray WedgeOfRays also creates a single Source object However this Source object defines a wedge shaped pattern of three rays In 23 wedgeofrays InputForm Out 23 InputForm Source SourceDescription gt SourceDescription WedgeOfRays Ray 10 SourceTransformation gt 0 0 0 1 0 0 0 1 O0 0 0 1 SymbolicSourceTransformation gt 0 0 0 1 0 0 0 1 0 0 0 1 SourceTransformation gt 0 0 0 1 0 0 0 1 0 0 0 1 SymbolicSourceTransformation gt 0 0 0 1 0 0 0 1 0 0 0 1 SourceLevel gt 1 1 NumberOfRays gt 3 BirthPoint gt 0 0 0 CoordinateSystem gt PolarCoordinates StartAtBirthPoint gt True MonteCarlo gt False SourceID gt 2118 SourceFraction gt 1 SourceOffset gt 0 GridSpacing gt 1 amp PowerOutput gt 100 SymbolicValues gt Next we will demonstrate how CreateRays is used by PropagateSystem to initialize the ray information as Ray objects When we apply CreateRays to wedgeofrays there are three Ray objects generated 1994 2005 Optica Software All rights reserved Rayica User Guide 13 In 22 CreateRays wedgeofrays InputForm Out 22 InputForm Ray Intensity gt 100 IntensityScale gt 1 OpticalMedium gt Air Polarization gt 0 1 0 RayEnd gt 0 0 0 RayLabelPositions gt 0 0 0 RayLength gt 0 RayLineRGB
33. Rayica User Guide 1 Introduction 3 Loading Rayica 3 A basic Rayica example 4 Inputting data 4 Modelling an optical system 5 Variable definition 5 Basic Commands 6 Using Options 7 Rayica s high level functions 8 2 Modeling Optical Components and Light Sources 9 Coordinates 9 Modeling a light source 9 Ray versus TurboRays 12 How Rayica manages default light source settings 14 Modeling an optical component 16 3 Introduction to the AnalyzeSystem and TurboPlot 18 4 The Move Function 19 5 Using AnalyzeSystem for Ray Tracing 20 Tracing a single ray 20 Working with the ray trace data 21 6 The ShowSystem Function 22 7 Tracing a Cone of Rays 24 8 Adding a Cylindrical Lens to the System 26 2 Rayica User Guide 9 The RayChoice Option 27 10 Using Screen to Look at the Focal Plane 29 11 The ShowRange Option 30 12 The ReadRays Function 30 13 The PropagateSystem Function 31 14 Using TurboPlot for Ray Tracing and Rendering 32 AnalyzeSystem versus TurboPlot 32 CreateClones 36 15 Optimization with OptimizeSystem 38 16 ReadRays with TurboTrace and TurboPlot 40 17 Energy Calculations with FindIntensity 40 2 D Calculations with FindIntensity 41 FindFocus 43 Measuring the Point Spread Function 45 Measuring the Modulation Transfer Function 46 1 D Calculations with FindIntensity 47 18 The Resonate Function 50 19 Rayica s Database 53 20 The TransferTraits Function 59 21 What s Missing 63 Features not discussed here 63 Featu
34. SCRIPTION OF OTHER RIGHTS AND LIMITATIONS 4a Limitations on Reverse Engineering Decompilation and Disassembly You may not reverse engineer decompile or disassemble the SOFTWARE PRODUCT except and only to the extent that such activity is expressly permitted by applicable law notwithstanding this limitation 4b Single User Restriction You are hereby granted a single user license for the SOFTWARE PRODUCT Unless otherwise expressly granted in writing by iCyt you agree to restrict use of the SOFTWARE PRODUCT to a specific single user on a single computer system You are expressly prohibited from copying duplicating or otherwise reproducing the software other than for archival purposes You may not install the SOFTWARE PRODUCT on a server or other computer device accessible by more than a specific single user unless access is strictly controlled to allow only that specific single user 4c Rental You may not rent or lease the SOFTWARE PRODUCT 4d Software Transfer You may permanently transfer all of your rights under this Agreement provided you retain no copies you trans fer all of the SOFTWARE PRODUCT including all component parts the media and printed materials any upgrades and this Agreement and the recipient agrees to the terms of this Agreement If the SOFTWARE PRODUCT is an upgrade any transfer must include all prior versions of the SOFTWARE PRODUCT 4e Termination Without prejudice to any other rights iCyt
35. SIBILITY OF SUCH DAMAGES 9 LIMITATION OF LIABILITY iCyt s entire liability and your exclusive remedy under this Agreement shall not exceed five dollars US 5 00 Lens Lab Rayica and Wavica are trademarks of Optica Software Copyright 2005 Optica Software and iCyt All rights reserved 1994 2005 Optica Software All rights reserved
36. a User Guide 41 cally carried out for each reported surface in two dimensions Because FindIntensity does not calculate interference or keep track of the coherent phase information it can only measure incoherent light flux properties 2 D Calculations with FindIntensity As an example we will plot the intensity present for a planar cross section of a Gaussian beam We will use FullForm gt True with the GaussianBeam function to generate a three dimensional pattern of rays FindIntensity uses the Plot2D option to specify how the intensity information is rendered With Plot2D gt False the intensity is rendered as a three di mensional plot PLot2D gt True constructs a two dimensional plot In addition the plot is colored according to the intensity levels present In 2 intensityresult FindIntensity GaussianBeam 10 1 NumberOfRays gt 64 FullForm gt True Move Screen 50 50 Plot2D gt False Surface Information ComponentNumber gt 1 SurfaceNumber gt 1 NumberOfRays gt 4096 SmoothKernelSize gt 2 38095 Surface Intensity 10 Out 2 ComponentNumber gt 1 Energy gt 100 Full3D gt True IntensityFunction gt CompiledFunction intensity data NumberOfRays gt 4096 OutputGraphics gt SurfaceGraphics RayBoundary gt 12 5 12 5 12 5 12 5 SmoothKernelSize gt 2 38095 SurfaceNumber gt 1 WaveFrontID gt 1 Note that since we specified NumberOfRays gt 64 with
37. adius is an option that specifies the radius of a Gaussian smoothing kernel Exp s42 radius 2 where s is distance along the surface In particular this smoothing kernel is convolved with another function in order to low pass filter its shape along a spatial surface SmoothKernelSize works together with the KernelScale option to smooth the calculated intensity function Here is the definition of KernelScale KernelScale gt Relative Absolute is used with FindIntensity to specify the form of the SmoothKernel1Size option KernelScale gt Relative indicates that the specified SmoothKernel1Size dimensions is a relative multiplicative factor of the minimum estimated spatial sampling dimension as determined from Nyquist sampling criteria KernelScale gt Absolute denotes that the specified SnoothKerne1Size dimensions are given in absolute spatial dimensions Measuring the Modulation Transfer Function Now that we have used FindIntensity to determine the point spread function of this lens system we can also calculate the ModulationTransferFunction of this system First we define ModulationTransferFunction ModulationTransferFunction intensitydata options calculates the modulation and phase transfer functions of an optical system for a given object source input ModulationTransferFunction works together with FindIntensity As input ModulationTransferFunction takes the returned output from FindIntensity T
38. and planar sources as long as the described imaging system contains a focus If a one dimensional light source is used ie WedgeOfRays Or LineOfRays then a one dimensional modulation transfer function is calculated If a two dimensional light source is used ie PointOfRays or GridOfRays then the optical transfer function calculations are carried out in two dimensions 1 D Calculations with FindIntensity Next we will examine a light sheet intensity calculation of the same optical system This is accomplished by setting Full Form gt False in GaussianBeam An initial trace of the optical system with TurboPlot reveals that the rays occupy a two dimensional plane 1994 2005 Optica Software All rights reserved 48 Rayica User Guide In 51 TurboPlot GaussianBeam 5 05 NumberOfRays gt 32 FullForm gt False SpotSizeFactor gt 2 Move ApertureStop 50 15 49 Move PlanoConvexLens 100 50 10 50 Move Screen 50 focalpoint PlotType gt Ful13D We will now apply FindIntensity to this system This time however we use NumberOfRays gt 1024 with Gaussian Beam With such a large number of rays FindIntensity can accurately model the geometric intensity properties of the light flux In addition we will use the ReportedSurfaces option to specify the optical surfaces that we are interested in measuring intensity In this case we specify ReportedSurfaces gt 1 1 3 1 to examine the first and third components In this c
39. are accessed with their function name given by Options function name In fact a good way to learn more about any unfamiliar function in Rayica or Mathematica is to have a look at its built in options because this often gives you a clue about the range of behaviors that the function can exhibit You can learn more about Rayica s built in light source functions in Section 1 3 4 of the Principles of Rayica Guide 1994 2005 Optica Software All rights reserved 16 Rayica User Guide Modeling an optical component Rayica has many more functions for modelling optical components than it has for light sources In fact there are presently 122 component functions in common use At any time that you wish while working with Rayica you can access a listing of the component functions with the ComponentFunctions command In 9 ComponentFunctions ABCDOptic AnamorphicPrisms ApertureStop AsphericLens AsphericLensSurface AsphericMirror Baffle BaffleSpan BaffleWithHole BallBaffle BallLens BallMirror BeamSplitter BeamSplitterCube BiConcaveCylindricalLens CustomDiffuserMirror LensDoublet RodMirror CustomFiber LensSurface RoofPrism CustomFiberMirror LensTriplet SchmidtLens CustomGrating LinearPolarizer SchmidtLensSurface CustomGratingMirror Mirror Screen CustomLens MirrorSpan SlabPrism CustomLensSurface ParabolicDiffuser SnowConeLens CustomMirror ParabolicDiffuserMirror SolidCornerCube C
40. ase each surface is specified with a list of two ordered numbers where the first number gives the component list order and the second number indicates a particular surface within the component grouping of surfaces 1994 2005 Optica Software All rights reserved Rayica User Guide 49 In 52 intensity FindIntensity GaussianBeam 5 05 NumberOfRays gt 1024 FullForm gt False SpotSizeFactor gt 2 Move ApertureStop 50 15 49 Move PlanoConvexLens 100 50 10 50 Move Screen 6 6 focalpoint ReportedSurfaces gt 1 1 3 1 Surface Information ComponentNumber gt 1 SurfaceNumber gt 1 NumberOfRays gt 1024 SmoothKernelSize gt 0 146041 Surface Intensity N A DH O O 10 5 5 10 Surface Information ComponentNumber gt 3 SurfaceNumber gt 1 NumberOfRays gt 616 SmoothKernelSize gt 0 00135192 Surface Intensity 000 000 000 20 1000 0 06 0 04 oi a 0 04 0 06 Out 52 ComponentNumber gt 1 Energy gt 100 Full3D gt False IntensityFunction gt CompiledFunction intensity data NumberOfRays gt 1024 OutputGraphics gt Graphics RayBoundary gt 12 45 12 45 SmoothKernelSize gt 0 146041 SurfaceNumber gt 1 WaveFrontID gt 1 ComponentNumber gt 3 Energy gt 98 3994 Full3D gt False IntensityFunction gt CompiledFunction intensity data NumberOfRays gt 616 OutputGraphics gt Graphics RayBoundary
41. ave a specific initial setting In such cases the optionvalue is given the same name as the optionlabel In other cases the optionvalue can simply be written as Automatic In such a case the option value is dynamically assigned Regardless of its setting every possible option parameter is listed in Options for the benefit of the user to know either that it exists or that it can be altered with a user specified value In order to specify a new ray parameter setting you simply pass the changed option setting as a parameter For example to change the wavelength setting to 0 633 microns you would use In 15 SingleRay WaveLength gt 633 Out 15 J SingleRay WaveLength gt 0 633 In this case a subsequent ray trace would use this new wavelength setting In addition SingleRay also has its own set of options that specifically applies to only the SingleRay function These are found in Options SingleRay In 3 Options SingleRay Out 3J NumberOfRays gt 1 BirthPoint gt Automatic SymbolicBirthPoint gt BirthPoint CoordinateSystem gt CartesianCoordinates StartAtBirthPoint gt True BalancePhaseFront gt True MonteCarlo gt False SourceOffset gt 0 SourceFraction gt 1 GridSpacing gt 1 amp IntensityFunction gt 1 amp PolarizationFunction gt 1 amp SourceID gt Automatic In the same manner as SingleRay all other built in light source functions also have their own specific option settings that
42. ay tracing without rendering the results you can use PropagateSystem when you are interested only in quantitative results without the pictures Here we use PropagateSystem together with ReadRays on the optical system shown previously In 29 screensystem PropagateSysten ConeOfRays 20 NumberOfRays gt 7 Move PlanoConvexLens 100 50 10 100 Move PlanoConvexCylindricalLens 100 50 50 10 130 Move Screen 50 50 218 Boundary 100 100 100 250 200 200 ReadRays screensystem OpticalLength ComponentNumber gt 3 Out 33 228 591 228 435 228 369 228 538 228 538 228 369 228 435 Because AnalyzeSystem performs both the ray tracing and rendering PropagateSystem is seldom used by the examples in this guide Nevertheless you can use PropagateSystem in precisely the same fashion as AnalyzeSystem for strictly numerical studies Next we will learn about TurboTrace and TurboPlot as high speed alternatives to PropagateSystem and AnalyzeSystem when large numbers of rays or trace iterations are required 1994 2005 Optica Software All rights reserved 32 Rayica User Guide 14 Using TurboPlot for High Speed Ray Tracing and Rendering In Version 1 AnalyzeSystem PropagateSystem were the only functions available for ray tracing Now however Rayica offers an entirely new suite of functions for high speed ray tracing of large ray data sets At the heart of this new capability is TurboTrace On most occasio
43. ayica that enable OptimizeSystem to perform global optimization See the Optica Software web site www opticasoftware com for further details We can now rerun TurboPlot with the information from soln to see a trace of the optimal result In 5 plot TurboPlot trace soln PlotType gt TopView As one final speed up we can add the option SequentialTrace gt True to OptimizeSystem Both OptimizeSystem and TurboTrace use SequentialTrace gt False by default In this case however we can use SequentialTrace gt True because the rays in this optical system are all passing through the same sequence of optical surfaces without back track ing or having multiple bounces In 4 Timing soln OptimizeSystem sphericalsystem SequentialTrace gt True Out 4 30 4 Second SymbolicValues gt rl gt 53 2884 r2 gt 106 975 NumberOfCycles gt 216 FinalMerit gt 0 0880703 1994 2005 Optica Software All rights reserved 40 Rayica User Guide In this final example SequentialTrace gt True has given us a further increase in speed With larger systems that have many optical surfaces there can be even greater gains in performance from this setting Although the example given here has optimized the surface curvatures of the lens many other optical parameters can be also optimized by simply assigning a symbolic value to each desired parameter This could include the thickness of a comp
44. ce a cylindrical lens directly behind the plano convex lens The cylindrical lens component is created with PlanoConvexCylindricalLens PlanoConvexCylindricalLens focallength aperture thickness options denotes a lens with a planar surface on one side and a convex cylindrical surface on the other side Here we use 50 50 in the aperture parameter of PlanoConvexCylindricalLens to make a rectangular edged cylindri cal lens In 56 opticalsystem AnalyzeSystem ConeOfRays 20 NumberOfRays gt 7 Move PlanoConvexLens 100 50 10 GraphicDesign gt Wire 100 Move PlanoConvexCylindricalLens 100 50 50 10 GraphicDesign gt Wire 130 Boundary 0 30 30 250 30 30 aN UNY AAN Z D LOA 4 pe Aan MARY AZ ew NA AQ 1994 2005 Optica Software All rights reserved Rayica User Guide 27 Again you can see different views of the system In 57 ShowSystem opticalsystem PlotType gt SideView Wr v yw Et 2 In 58 ShowSystem opticalsystem PlotType gt TopView Et t2 Notice that in the two previous graphics Rayica has automatically attached labels to the two lenses L1 and L2 This feature can be helpful to make illustrations in publications You can learn more about Rayica s treatment of graphics in Chapter 6 of the Principles of Rayica Guide You can make exact positional measure
45. culation nor does any other function for that matter It is always valuable to check a functions definition to see whether or not an input element is required for calculation or not 1994 2005 Optica Software All rights reserved Rayica User Guide 5 Modelling an optical system When entering an optical system into Rayica you should consider what elements to include To produce any meaningful result it is necessary to have two things light sources and optical components More often than not you will have only one light source but several components though only one of each has been included in this example The light source is LineOf Rays and the optical component is PlanoConvexLens Another essential element of this system is the Screen While not an optical element per se the Screen provides a necessary function in that it intercepts all rays which come in contact with it without changing the optical properties of the ray Just as important as the components and light sources that you include in an optical system is their position in the system As such you will make almost constant use of the Move function Move allows any object to be moved to any location or position within an optical system For more information on the Move function and its uses see Section 4 of this guide The ultimate use of an optical system in Rayica is analysis and or display If you are unsure of the function that you wish to use to analyze the optical
46. culation process This section has provided a glimpse of new capabilities now made possible with TurboPlot and CreateClones In the next section we will see how OptimizeSystem makes optimization problems easy to manage in Rayica 15 Optimization with OptimizeSystem Previously we learned how to incorporate used defined symbolic parameters into optical systems In particular we saw how to assign a symbolic focal length to a lens and then assign different numeric values for different ray trace calculations Opt imizeSystem also uses such symbolic parameters in order to iteratively optimize some aspect of an optical system OptimizeSystem system options optimizes the performance of an optical system for a specified set of symbolic input parameters While in its default operation OptimizeSystem tries to minimize the ray locus spot size on a last surface of the optical system you can also customize OptimizeSystem for nearly any other characteristic that you wish In this section however we will stick with the default settings of OptimizeSystem to find the best focus for a lens system Next we will create a double surface lens with the SphericalLens function SphericalLens r r2 aperture thickness options denotes a lens having two spherical surfaces with radius of curvatures given by r and r2 In this case we will use two symbolic parameters r1 and r2 to represent the radius of curvature of each le
47. cussion or even within the scope of a basic user manual It is the expectation of the author that Rayica s documentation will by necessity be an on go ing endeavor that is continually updated as a result of feedback from the Rayica user community For this purpose a new Optica Software web site www opticasoftware com has been erected to provide on line documentation additional exam ples up to date software and advanced technical support Features not covered in the basic package It is important to consider which features are not built into the basic Rayica package In particular Rayica does not model the following wave front propagation coherent point spread functions analytical solutions to optical systems and Gaussian optics paraxial analysis Although Rayica can model diffraction gratings its does not model diffractive behavior in general These items are instead a part of a separate package called Wavica In the future Rayica and Wavica may be combined into a single package but at the moment they are distributed separately although they work together seamlessly The basic Rayica system is therefore limited to three dimensional geometric ray trace calculations intensity measurements publica tion illustrations and optimizations However Rayica s geometric results do contain information about the optical path length and from this it is possible to calculate the optical phase information on a surface This is demonstrated in Sec
48. dex gt 1 46008 DesignWaveLength gt 0 5461 FileName gt Melles m FocalLength gt 75 0089 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 34 51 SurfaceBoundary gt 50 50 SurfaceSeparation gt 13 8 CatalogNumber gt LQP005 CenterThickness gt 13 8 CompanyName gt MellesGriot ComponentBoundary gt 50 ComponentLabel gt UVGradePlanoConvex ComponentMedium gt FusedSilica Date gt 1999 4 18 DesignRefractiveIndex gt 1 46008 DesignWaveLength gt 0 5461 FileName gt Melles m FocalLength gt 75 0089 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 34 51 SurfaceBoundary gt 50 50 SurfaceSeparation gt 13 8 CatalogNumber gt PCX45246 CenterThickness gt 11 CompanyName gt EdmundScientific ComponentBoundary gt 50 ComponentLabel gt PlanoConvex ComponentMedium gt BK7 Date gt 1999 4 18 DesignRefractiveIndex gt 1 51678 DesignWaveLength gt 0 588 FileName gt Edmund m FocalLength gt 75 0027 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 38 76 o SurfaceBoundary gt 50 50 SurfaceSeparation gt 11 BackFocalLength gt 66 3 CatalogFocalLength gt 75 CatalogNumber gt FPX11730 000 CenterThickness gt 12 7 CompanyName gt JML ComponentBoundary gt 50 ComponentLabel gt PlanoConvexLens ComponentMedium gt Quartz Date gt 1999 4 18 DesignWaveLength gt 587 6 EdgeThickness gt 1 9 FileName gt JML m
49. e is made up of two folders Rayica and RayicaTools The Rayica folder contains all of the essential files that make up Rayica while RayicaTools contains auxiliary functions for loading packages and working with Mathemat ica Make sure that both the Rayica and RayicaTools folders are located together in a directory path recognized by Mathemat ica for packages The Rayica package is loaded with the following command In 1 Needs Rayica Rayica FHFEEFEFEEET EF EE TH 4 444444 Rayica 2 0 was loaded in 18 s and needs 6019 kilobytes of memory on top of 3499 kilobytes already used This loading process can take a minute or two depending on your computer s speed In addition to being loaded as a package all of Rayica files are formatted as Mathematica notebooks The Rayica source code is made accessible in the Rayica folder so that you can develop new functions of your own by studying Rayica s built in functions This is particularly helpful when you wish to model new component ideas in Rayica 1994 2005 Optica Software All rights reserved 4 Rayica User Guide A basic Rayica example The simplest way to learn Rayica is to experiment with its text based interface To this end we have included a series of examples based on a simple optical system in this Introduction of the User Guide The following series of examples will be used to demonstrate the elements necessary to create and analyze a basic optical system in Rayica Each line of
50. ecify all possible parameters required by the function to operate Such default parameters are referred to as options because you can optionally decide to change the setting of such a parameter but you don t have too As you will see shortly each option follows the pattern optionlabel gt optionvalue Such a pattern is also called a rule because it is internally evaluated by Mathematica as Rule optionlabel optionvalue As with all other types of Rayica s light source functions SingleRay has many options that help describe the generated ray Since all types of light sources must make the same basic assumptions about their created rays Rayica uses a single location called Options Ray to store this information The most important of these settings include physical attributes such as wavelength polarization intensity and optical length However there are also a number of other non physical attributes as well You can check these default assumptions by examining the contents of Options Ray 1994 2005 Optica Software All rights reserved Rayica User Guide 15 In 4 Options Ray Out 4J ComponentIncrement gt Automatic ComponentNumber gt ComponentNumber ConfinedNumber gt ConfinedNumber ConfinedPosition gt ConfinedPosition DiffractionMismatch gt DiffractionMismatch DiffractionOrderNumber gt DiffractionOrderNumber GenerationNumber gt GenerationNumber Intensity gt 100 InternalDirectionChange gt
51. ensions for a prism CompanyName gt name gives the name of a component manufacturer FocalLength gt focallength specifies the effective focal length of a lens RayicaFunction gt functionhead specifies the Rayica function used to create a model representation of the database item in Rayica OpticalMedium gt symbol identifies the optical material medium traversed by each ray segment Some important database parameters Of these different database parameters the RayicaFunction is of particular importance because it declares the purpose of the database entry to Rayica As such every database entry usually contains RayicaFunction as a parametername We can use ReadData with RayicaFunction to list the declared types of database entries that are present in Rayica s database In 35 ReadData RayicaFunction ReportedInterval gt All Union gt True Out 35J AnamorphicPrisms AsphericLens BallLens BeamSplitter BeamSplitterCube BiConcaveLens BiConvexLens CompoundLens CustomMirror CylindricalLens DirectVisionPrism DovePrism FresnelRhomb HerzbergerFunction HollowCornerCube IndexFunction IndexInterpolationFunction JonesMatrixOptic LensDoublet LensTriplet LinearPolarizer Mirror ModelRefractiveIndex ParabolicMirror PechanPrism PentaPrism PlanoConcaveCylindricalLens PlanoConcaveLens PlanoConvexCylindricalLens PlanoConvexLens PolarizingBeamSplitterCube PorroPrism Prism RetardationPlate ReversionPrism R
52. ersion 1 you can call SetOptions with Move as shown SetOptions Move RayicaVersion gt 1 Here the default setting is RayicaVersion gt 2 In order to recover many of the default option behaviors from the original Optica edition including the original Move behaviors you can call SetOptions with Rayica as shown SetOptions Rayica RayicaVersion gt 1 New Function Name Alias AnalyzeSystem for DrawSystem Previous users of Optica will notice that the new version has adopted a new naming alias for DrawSystem that is called AnalyzeSystem Nevertheless the original DrawSystem still exists and works the same as before The only change in AnalyzeSystem is that the Options AnalyzeSystem contains a reduced subset of the Options DrawSystem in order to reduce option clutter New Parametric Surface Function Format A new format can now be used to specify parametric surfaces in Rayica While the original parametric format for Rayica required a distinct Function to specify each spatial coordinate direction the new format embeds all three coordinates within a single Function head In particular Function 5 7 xcoordinate s t ycoordinate s t zcoordinate s t can now be used instead of Function s t xcoordinate s t Funetion s t ycoordinate s t Function s t zcoordinate s t New Grating Vector Format There is a new coordinate order used to specify grating vectors in Rayica The grating vector now has a different coordina
53. fRays seed size options initializes a set of rays distributed on the surface of a tube that points down the positive x axis ConeOfRays Seed spread options initializes a set of rays distributed along a funnel shaped surface that is oriented down the positive x axis WedgeOfRays seed spread options initializes a set of rays in the x y plane that fan out with their chief direction oriented down the positive x axis and are distributed across the y coordinate with the specified fan spread LineOfRays seed linewidth options initializes a set of rays in the x y plane that point down the positive x axis and are distributed along the y coordinate with the specified linewidth GridOfRays seed size options initializes a set of rays distributed throughout a tube shaped volume that points down the positive x axis PointOfRays seed spread options initializes a set of rays distributed throughout a funnel shaped volume that is oriented down the positive x axis CustomRays seed name vector options initializes a set of user defined rays GaussianBeam beamspotsize fulldivergence options and GaussianBeam complexbeamparameter options is a light source that takes either the output beam spotsize radius specified at 1 e of the axial value of the electric field amplitude peak in the starting plane and far field beam fulldivergence specified as the full angle in radians at 1 e42 or the complex beam parameter as input and creates a
54. face Intensity 0 1 0 05 0 05 0 1 1994 2005 Optica Software All rights reserved 46 Rayica User Guide The last intensity plot is taken at the focal plane of the system and shows the point spread function FindIntensity works by convolving a Gaussian smoothing kernel with the ray trace data However the result may not accurately depict the diffractive performance of the system In particular FindIntensity automatically adjusts the smooth kernel size to maxi mize the measurement resolution to the available ray density In this way if the number of input rays are sufficiently great FindIntensity models the geometric behavior of the system However you can approximate some effects of the diffrac tion performance if you have independent knowledge of the diffraction limited spot size for the system In this case you can manually set the SmoothKernelSize option to correspond with the diffraction limited spot size of the optical system together with KernelScale gt Absolute In that case the intensity plot generated by FindIntensity can depict both the geometric and incoherent diffractive properties of a system However if the SmoothKernelSize is manually set it is always necessary that make sure that there are a sufficient number of rays are present in order to meet the Nyquist sampling criterion Otherwise the resulting calculation will not be correct Here is the definition of SmoothKernelSize SmoothKernelSize gt r
55. frequently required As such we will now examine the PlotType option in more detail PlotType is an option of AnalyzeSystem ShowSystem and TurboP1lot that designates the display form of the graphics rendering for the optical system PlotType can take eight different settings as listed below TopView gives a two dimensional orthoscopic rendering showing a projection onto the x y plane of the optical system FrontView gives a two dimensional orthoscopic rendering showing a projection onto the y z plane of the optical system SideView gives a two dimensional orthoscopic rendering showing a projection onto the x z plane of the optical system Fu113D gives the full three dimensional rendering of the optical system RealTime3D allows the rendered three dimensional graphics to be rotated interactively off designates no graphical output Surface gives a two dimensional plot that shows selected intersection points between rays and one or more optical surfaces ShadowProject gives a three dimensional rendering of the optical system along with two dimensional projections of the system onto the sides of a box Settings of Plot Type Finally we will demonstrate ShowSystem once again with the same trace result This time however we will use Plot Type gt RealTime3D This option setting allows you to interactively rotate the ray trace plot in three dimensions with the mouse 1994 2005 Optica Software All ri
56. function Before continuing with the ray trace lets first examine the Boundary function in more detail Boundary boundaryparameters denotes a rectangular box that absorbs rays intercepted by its walls There are three methods for specifying boundaryparameters Boundary x yl zl x2 y2 z2 uses the coordinates of top and bottom opposite corners of a rectangular box Boundary side assumes a cube boundary and Boundary aside bside assumes a three dimensional box having a length specified by aside a width specified by bside and a height specified by bside Optical systems propagating rays usually have at least one boundary component listed at the end In this example we will use Boundary 200 1994 2005 Optica Software All rights reserved Rayica User Guide 21 We can now use AnalyzeSystem for ray tracing For this we will trace a single ray through a lens using the SingleRay PlanoConvexLens and Boundary functions This time we will store the ray trace result in a variable called trace This will allow us to examine the traced information later on with other functions In 22 trace AnalyzeSysten SingleRay Move PlanoConvexLens 100 50 10 100 10 45 Boundary 200 70 AnalyzeSystem SingleRay Move PlanoConvexLens 100 50 10 100 10 45 Boundary 0 35 35 200 35 35 Out 22 3 ray surface intersections By default Rayica always takes the x axis
57. ght sources to options Almost anything that can be evaluated by Mathematica can be defined using the command Another very useful command is the command Use of is discussed in the 10 minute introduction to Mathematica which you may wish to read Essentially acts as a variable which stores the result of the previous calculation So if you wish to use the results of the last calculation performed simply create a new input using and evaluate it 1994 2005 Optica Software All rights reserved Rayica User Guide 7 The final fundamental command is Options When you enter a Rayica function name into the square brackets and press Shift Enter a list of the options associated with that function name are displayed Finding a rule and applying it will be discussed in the next section In 12 Options Screen Out 12 Labels gt S LabelPositions gt Automatic ComponentDescription gt Automatic Transmittance gt 100 GraphicDesign gt Automatic Automatic gt SurfaceRendering gt Trace CrossRendering gt Trace Sketch gt SurfaceRendering gt Trace CrossRendering gt Trace Wire gt SurfaceRendering gt Mesh CrossRendering gt Empty Solid gt SurfaceRendering gt Fill Trace CrossRendering gt Empty Using Options Options are available for almost every element of Rayica To discover what options are associated with the elements that you are using use the Options command as discussed in the
58. ghts reserved 24 Rayica User Guide In 10 ShowSystem trace PlotType gt RealTime3D You can use the mouse to interactively grab and rotate this three dimensional graphic in real time Before concluding this brief introduction to ShowSystem there is one final comment worth mentioning about the use of ShowSystem with TurboPlot results Although you can always use ShowSystem to render results created by TurboPlot ShowSystem will normally call TurboPlot to render TraceTrace data rather than doing the work itself This is because ShowSystem is not efficient at directly displaying the large numbers of rays that are often associated with TurboPlot calculations TurboPlot on the other hand is optimized for the rendering of TurboTrace results This will be demon strated in Section 14 7 Tracing a Cone of Rays To propagate several rays through a lens you can use one of Rayica s other built in ray source functions Here we use ConeOfRays with AnalyzeSystem In 5 AnalyzeSystem ConeOfRays 20 NumberOfRays gt 7 Move PlanoConvexLens 100 50 10 100 Boundary 0 25 25 200 25 25 1994 2005 Optica Software All rights reserved Rayica User Guide 25 Note that this time in order to position the PlanoConvexLens we have passed the single numeric parameter of 100 to the Move function When only single number is given to Move the PlanoConvexLens is simply displaced along the x axis by the given amount Yo
59. gt 0 0692861 0 0692861 SmoothKernelSize gt 0 00135192 SurfaceNumber gt 1 WaveFrontID gt 1 Here we see that reported Energy information shows a decrease in the transmitted energy between the first and last reported surface In particular there is a slight loss as a result of the aperture stop With this particular system the Fresnel losses associated with refractive lens surfaces are not taken into account However you could use the FresnelReflections gt True option with PlanoConvexLens to include this effect as well The FresnelReflections option is examined in Section 3 4 2 of the Principles of Rayica discussion 1994 2005 Optica Software All rights reserved 50 Rayica User Guide We can again use ModulationTransferFunction with our FindIntensity result This time however we need to pass only the information from the focal surface In addition we can abbreviate the ModulationTransferFunction command with MTF In 53 MTF intensity 2 Modulation 0 25 50 75 100 125 150 175 Out 53 ComponentNumber gt 3 Energy gt 98 3994 FrequencyCutoff gt 184 922 Full3D gt False ImageSampleSize gt 0 00261457 IntensityFunction gt CompiledFunction intensity data ModulationTransferFunction gt InterpolatingFunction 0 190 371 lt gt NumberOfPoints gt 54 NumberOfRays gt 616 OutputGraphics gt Graphics PhaseTransferFunction gt InterpolatingFunction 0 190 37
60. gt 2 7 0 CatalogNumber gt 34 2972 CenterThickness gt 7 CompanyName gt Coherent Ealing ComponentBoundary gt 25 4 ComponentLabel gt plano convex lens ComponentMedium gt Quartz Date gt 1999 4 18 DesignRefractiveIndex gt 1 45843 DesignWaveLength gt 0 5876 FileName gt CoherentEaling m FocalLength gt 38 06 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 17 45 SurfaceBoundary gt 25 4 25 4 SurfaceSeparation gt 7 0 In general you can use many different formats for conducting a search in the Rayica s database Such formats include strings rules lists of numbers and symbols In this past example we have searched for the PlanoConvexLens symbol We could have instead searched for RayicaFunction gt PlanoConvexLens However this turns out to be unnecessary since PlanoConvexLens is only used with the RayicaFunction in the database From this result we can see that there are about 15 separate parameternames available for the PlanoConvexLens entry We can now decide on the top 2 or 3 most impor tant parameternames for a more specialized search For example we can search for specific values of ComponentBoundary and FocalLength 1994 2005 Optica Software All rights reserved Rayica User Guide 57 In 73 SearchData PlanoConvexLens ComponentBoundary gt 50 FocalLength gt 65 Out 73 BackFocalLength gt 53 9 CatalogFocalLength gt 65 CatalogNumber gt FPX11700
61. han AnalyzeSystem Propa gateSystem when only a small number of rays are traced However if a larger number of rays are needed or if many trace iterations are required then TurboTrace based calculations are always the best way to go As an example consider the following optical system In 3 system GaussianBeam 10 1 NumberOfRays gt 11 FullForm gt True Move PlanoConvexLens 100 50 10 50 Move Screen 50 150 This example uses the GaussianBeam light source function GaussianBeam simulates the intensity and optical phase characteristics of a Gaussian laser beam see Section 2 In our system the spot size and beam divergence were given by 10 and 1 respectively Here we used the FullForm gt True option to specify a three dimensional pattern of rays Other wise with the default setting of FullForm gt False GaussianBeam only creates a fan of rays within a light sheet Since we specified NumberOfRays gt 11 with FullForm gt True in the GaussianBean there will be in fact 117 121 rays created This is because for three dimensional sources NumberOfRays refers to the number of rays along each dimension of the ray cross section If FullForm gt False were used instead to construct a two dimensional fan of rays then only 11 rays would have been initiated in total AnalyzeSystem versus TurboPlot Let us first trace this system with AnalyzeSysten to get a timing baseline and then follow this up with the use of Turb
62. haps the most important format changes have been with the Move functions These changes to Move are discussed next Moves3D is now obsolete It is no longer necessary to use separate functions for three dimensional positioning In particular Move3D MoveLinear3D MoveDirect3D and MoveReflected3D functionalities have now been absorbed by the Move MoveLinear MoveDirect and MoveRef lected functions However the original 3D functions will continue to be supported in the new Rayica edition Move object x y z now works There is a new pattern of Move called Move object x y z that gives a simple three dimensional translation Unfortu nately this new pattern conflicts with an older pattern of Move and can create a legacy problem for some pre existing system designs made in original Optica edition This is explained further next Move object x y angle has become Movef object x y angle Move object x y rotationangle has now been superseded by Move object x y rotationangle This change has been made in order to support the Move object x y z format shown previously Unfortunately this has adverse implications for any legacy code that used Move object x y rotationangle 1994 2005 Optica Software All rights reserved Rayica User Guide 65 How to recover version 1 behaviors Some of Rayica s new behaviors are irreversible However if you are interested to recover the original Move behaviors of V
63. he optical system must contain a light source followed by the imaging optics with the focal surface as its last element In 49 Options ModulationTransferFunction out 49jJ SpatialScale gt 1 FrequencyCutoff gt Automatic PaddingFactor gt 7 NormalizePlot gt True InterpolationOrder gt 1 PlotPoints gt 40 Plot2D gt True ContourLines gt False Contours gt 50 ColorFunction gt Hue 0 65 10 65 1 10 9 0 1 amp RenderedParameters gt ModulationTransferFunction 1994 2005 Optica Software All rights reserved Rayica User Guide 47 In 50 ModulationTransferFunction focusintensity Modulation 0 5 10 15 20 Out 50j ComponentNumber gt 3 Energy gt 99 257 FrequencyCutoff gt 23 8254 23 8254 Full3D gt True ImageSampleSize gt 0 01499 0 020986 IntensityFunction gt CompiledFunction intensity data ModulationTransferFunction gt InterpolatingFunction 33 3555 32 3132 23 8254 22 8724 lt gt NumberOfPoints gt 8 6 NumberOfRays gt 956 OutputGraphics gt SurfaceGraphics ModulationTransferFunction gt Graphics PhaseTransferFunction gt InterpolatingFunction 33 3555 32 3132 23 8254 22 8724 lt gt RayBoundary gt 0 0524651 0 0524651 0 0524651 0 0524651 SmoothKernelSize gt 0 020986 SurfaceNumber gt 1 WaveFrontID gt 1 ModulationTransferFunction works equally well for both point sources
64. homboidPrism RoofPrism SellmeierFunction SolidCornerCube SphericalLens SphericalMirror WedgeBeamSplitter WedgePrism Window 1994 2005 Optica Software All rights reserved 56 Rayica User Guide Here we used ReportedInterval gt A11 to retain all of the valid elements from the database search Otherwise Rayica truncates the search result to the first 1000 elements The Union gt True option is then used to generate a logical union of the results From this we see that most of the database items are used with component function entries such as PlanoCon vexLens Prism and Mirror The remaining items such as IndexFunction are used with optical material entries When you wish to search for a particular optical component often a good starting point is to use the official name of the component function in Rayica such as PlanoConvexLens You can then use SearchData to do a search for this name to discover which other attributes are listed with it You can then narrow your search further with some of these attributes It is good idea to first limit the total number of reported elements with ReportedInterval Otherwise the reported number of entries can be overwhelming Here is a description of ReportedInterval ReportedInterval is an option that restricts the total number of items getting reported by a function In general ReportedInterval can take several different formats ReportedInterval gt reportednumber
65. ica s positioning directives The most important positioning directive in Rayica is the Move function You can use Move to position both light sources and rays in space The basic definition for Move is shown below Move objectset x y rotationangle options is used to move the relative position and orientation of a set of components and rays within a horizontal plane Here the rotationangle determines the angular orientation of the object set within the horizontal plane You can use the TwistAngle gt angle option to specify a rotation angle around the axis of orientation Next we will use Move together with AnalyzeSystem to draw two lenses spaced apart from each other Place the first one at x 0 y 0 with no rotation and a second one at x 100 y 10 with a 45 degree rotation In 21 AnalyzeSysten PlanoConvexLens 100 50 10 Move PlanoConvexLens 100 50 10 100 10 45 Axes gt True AnalyzeSystem PlanoConvexLens 100 50 10 Move PlanoConvexLens 100 50 10 100 10 45 Out 21 rendered system without rays 1994 2005 Optica Software All rights reserved 20 Rayica User Guide Note that again the text output returned to the screen mimics the original input expressions when in fact a great quantity of information is hidden behind the rendered system without rays statement Although only a single format has been shown previously for Move there are actually a va
66. in component functions of Rayica to describe complex optical elements such as multi faceted prisms Since many optical systems do require non sequential ray interactions between multiple component surfaces Resonate is one of the most important functions in Rayica Here we define Resonate Resonate listofcomponents options causes a ray to be nonsequentially traced within all of the surfaces defined by listofcomponents 1994 2005 Optica Software All rights reserved Rayica User Guide 51 Rayica always traces rays between distinct optical components in a sequential fashion This means that the ray trace is always occurring in the same sequence as the component list order However anytime the ray trace occurs within the sur faces of an optical component such as a Prism then non sequential ray tracing becomes possible In some cases however it becomes necessary for rays to travel non sequentially between one or more components For this purpose you can use Resonate Lets take for an example the case of a lens mirror combination Here the rays might travel through a lens reflect off a mirror and then travel back through the same lens for a second pass In its normal mode of operation Rayica does not see the lens on the second pass when the components are listed separately In 81 AnalyzeSystem LineOfRays 45 Move PlanoConvexLens 100 50 10 50 Move Mirror 50 5 75 Boundary 100 PlotType gt TopView
67. indicates an upper limit to the number of items getting reported ReportedInterval gt startnumber endnumber gives both lower and upper bounds to the number of items getting reported ReportedInterval gt Interval min max can also be used In the next example we use ReportedInterval gt 3 to limit the length of the result to 3 elements In this particular search we will use PlanoConvexLens to seek out database entries that relate to plano convex lenses In 68 SearchData PlanoConvexLens ReportedInterval gt 3 Out 68J CatalogNumber gt 34 2949 CenterThickness gt 3 4 CompanyName gt Coherent Ealing ComponentBoundary gt 12 7 ComponentLabel gt plano convex lens ComponentMedium gt Quartz Date gt 1999 4 18 DesignRefractiveIndex gt 1 45843 DesignWaveLength gt 0 5876 FileName gt CoherentEaling m FocalLength gt 25 37 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 11 63 SurfaceBoundary gt 12 7 12 7 SurfaceSeparation gt 3 4 0 CatalogNumber gt 34 2964 CenterThickness gt 2 7 CompanyName gt Coherent Ealing ComponentBoundary gt 12 7 ComponentLabel gt plano convex lens ComponentMedium gt Quartz Date gt 1999 4 18 DesignRefractiveIndex gt 1 45843 DesignWaveLength gt 0 5876 FileName gt CoherentEaling m FocalLength gt 38 06 OpticaFunction gt PlanoConvexLens RadiusOfCurvature gt 17 45 SurfaceBoundary gt 12 7 12 7 SurfaceSeparation
68. ing repetitive optical elements This feature is not present in AnalyzeSystem although you can still display the results with ShowSystem if you wish This capability is managed with the CreateClones option CreateClones gt coordinates rotationmatrix componentnumber scale specifies the placement of one or more phantom optical components to be used during the ray trace These component aliases exhibit the ray trace behavior of the original component members but do not consume additional computer memory This permits the efficient nonsequential ray tracing of large arrays of optical elements CreateClones accepts a wide range of data structures for managing different forms of repetitive elements With the most general format of CreateClones it is possible to specify different three dimensional coordinates orientations via rotation matrix and sizes via scale for every repeated element In addition you can specify a mixture of different components in CreateClones by passing the corresponding componentnumber of each template element For the purposes of this discussion however we will only demonstrate the simplest possible formulation for CreateClones In particular we will specify the x y coordinates for different clone positions along the x and y dimensions of space and we will not alter the relative size or orientation of the cloned elements As such we need only to construct a list of two dimensional positions f
69. may terminate this Agreement if you fail to comply with the terms and conditions of this Agreement In such event you must destroy all copies of the SOFTWARE PRODUCT and all of its component parts 5 EXPORT RESTRICTIONS You agree that neither you nor your customers intend to or will directly or indirectly export or transmit a the SOFTWARE PRODUCT or related documentation and technical data or b any Application developed with the SOFTWARE PRODUCT or any part thereof or process or service that is the direct product of the SOFTWARE PRODUCT to any country to which such export or transmission is restricted by any applicable U S regulation or statute without the prior written consent if required of the Bureau of Export Administration of the U S Depart ment of Commerce or such other governmental entity as may have jurisdiction over such export or transmission 1994 2005 Optica Software All rights reserved 68 Rayica User Guide 6 U S GOVERNMENT RESTRICTED RIGHTS SOFTWARE PRODUCT and documentation are provided with RESTRICTED RIGHTS Use duplication or disclosure by the Government is subject to restrictions as set forth in subparagraph c 1 ii of The Rights in Technical Data and Computer Software clause at DFARS 252 227 7013 or subparagraphs c 1 and 2 of the Commercial Computer Software Restricted Rights at 48 CFR 52 227 19 as applicable Manufacturer is iCyt an Illinois corporation 7 MISCELLANEOUS If
70. me initial compari sons between these two methods we will next consider the use of AnalyzeSystem The application of TurboPlot will be explored further in Section 15 AnalyzeSystem objectset options uses PropagateSystem and ShowSystenm to trace rays through optical components and render the results TurboP1lot system options works with TurboTrace to perform accelerated ray tracing and rendering of a system of light sources and optical elements Both AnalyzeSystem and TurboPlot call other intermediate functions for their internal operations of ray tracing and graphical rendering They simply provide a single convenient interface for the Rayica user to conduct the ray tracing and rendering Both AnalyzeSystem and TurboPlot are used in the same fashion as each accepts a list of light source and component functions for input One key difference between AnalyzeSystem and TurboP1ot is that AnalyzeSystem uses the interpreted language of Mathematica for ray tracing while TurboPlot uses a highly efficient compiled function which is more time consuming to create initially but then performs the actual ray trace much faster As a result of this when only a small number of rays are needed AnalyzeSystem can sometimes deliver a result more quickly than TurboPlot In addi tion AnalyzeSystem often works better than TurboPlot for the creation of optical schematics and illustrations for publica tion since it is tailored for such purposes Howeve
71. ments in the two dimensional fields by clicking the graphics display cell and then holding down the Command key while moving the cursor over the image The cursor coordi nates are displayed in the bottom corner of the window More accurate measurements can be taken by expanding the graphic display size By examining the TopView image you can measure the focus position to be x 218 millimeters 9 The RayChoice Option You can use the RayChoice option to display portions of the ray tracing result Here we define RayChoice RayChoice gt selectionproperties uses selectionproperties to selectively display ray segments in AnalyzeSystem and ShowSystem Next we will use RayChoice to examine the ray segments after the cylindrical lens in the system Use RayChoice gt Compo nentNumber gt 3 to view the ray segments immediately following the cylindrical lens In general you can use Component Number with RayChoice to choose ray segments associated with any particular component 1994 2005 Optica Software All rights reserved 28 Rayica User Guide In 61 ShowSystem opticalsystem RayChoice gt ComponentNumber gt 3 You can also use Plot Type gt Surface with RayChoice to look at the ray intersection points on any surface in the ray trac ing result We now define Surface Surface is a value of Plot Type giving a two dimensional plot showing selected intersection points between rays and one or more optical s
72. ms Rayica how create the required rays at the start of the ray trace In particular the Source object indicates which type of function has created it SingleRay in this case and includes special instructions about how many rays are to be created as well as how to configure the created rays into a particular spatial pattern All of Rayica s light source functions generate a Source object in the same fashion as SingleRay Each light source function always creates a single Source object regardless of the actual number of rays used in the trace After a ray trace has been carried out specific information is usually returned about the optical surface intersections encountered by the rays in the trace However Source objects are only used to initiate the trace and are not used to store the resulting information from the ray trace Instead the traced rays are stored either as Ray objects with AnalyzeSystem Prop agateSystem or as TurboRays objects with TurboPlot TurboTrace In the next section you will learn more about Ray and TurboRays objects and how they get created from Source objects by the ray trace functions of Rayica 1994 2005 Optica Software All rights reserved 12 Rayica User Guide Ray versus TurboRays In this section we will examine how PropagateSystem and TurboTrace store ray information as either Ray or Turbo Rays objects In general however the user of Rayica will never work directly with Ray and TurboRays objects As such
73. n extended point source ray model of a Gaussian laser beam Rainbow0OfRays Seed minwavelength maxwavelength options initializes a set of overlapping rays that point down the positive x axis and are distributed over the specified range of wavelengths given in microns Ten commonly used light source functions At any time that you wish while working with Rayica you can access a listing of Rayica s main high level light source functions with the SourceFunctions command In 8 SourceFunctions CircleOfRays LineOfRays ConeOfRays PointOfRays CustomRays RainbowOfRays GaussianBeam SingleRay GridOfRays WedgeOfRays In Mathmatica SourceFunctions gives you hyperlinks to Rayica s most important light source functions Clicking on any name will give you a description of its use Most light sources in Rayica generate multiple rays of light However the simplest type of light source is the SingleRay function This is designed for applications that require a single ray to be traced When multiple rays are required you could in principle specify a list of SingleRay functions for each ray but it is always faster and more memory efficient to use one of the other built in light source functions instead In Rayica each light source function generates the information needed to describe a particular pattern of geometric rays You can either store this generated information in an intermediate variable or immediatel
74. ns as with PropagateSystem TurboTrace is not called directly by the user Instead either TurboPlot OptimizeSystem or FindIntensity is employed In this section we will examine TurboPlot Then in Sections16 and 17 OptimizeSystem and FindIntensity will be discussed TurboTrace optics options produces an accelerated ray trace of a system of light sources and optical elements TurboP1lot optics options works with TurboTrace to perform accelerated ray tracing and rendering of a system of light sources and optical elements On the outside TurboPlot behaves in much the same fashion as AnalyzeSystem In particular TurboPlot also accepts a list of light source and optical component functions for its input traces the rays through the components and renders the results TurboPlot also uses many of the same options as AnalyzeSystem and ShowSystem for rendering its information Internally however TurboTrace and TurboPlot are designed with one objective in mind namely speed For its ray trace calculations TurboPlot depends on TurboTrace just as AnalyzeSystem uses PropagateSystem When it is called with a new optical system TurboTrace first constructs a compiled function called a RayTraceFunction that performs the ray trace calculation and is returned as a part of the ray trace result Initially this construction process can consume a signifi cant amount of time and for this reason TurboPlot TurboTrace can sometimes be slower t
75. ns surface In 2 sphericalsystem GaussianBeam 10 1 NumberOfRays gt 11 Move SphericalLens r1 100 r2 100 50 10 50 Move Screen 50 150 1994 2005 Optica Software All rights reserved Rayica User Guide 39 OptimizeSystem uses the numeric value that accompanies every symbolic parameter as an initial starting value for the numeric minimization process As a user you can influence the minimization process through your choice of these settings In this case the initial numeric setting for r1 is 100 mm and for r2 is 100 mm When we call TurboPlot directly we can trace of the lens system with its initial numeric settings In 3 Timing trace TurboPlot sphericalsystem PlotType gt TopView Out 3J 7 83333 Second traced system Finally we call OptimizeSystem with the untraced sphericalsystem information In 4 Timing soln OptimizeSystem sphericalsystem Out 4 36 15 Second SymbolicValues gt rl gt 53 2884 r2 gt 106 975 NumberOfCycles gt 216 FinalMerit gt 0 0880703 Here we have stored the resulting answer from OptimizeSystem in the soln variable In this case the system was itera tively traced 216 times before the optimal value was determined Note that the standard OptimizeSystem cannot always find the global minimum and may only find a local minimum In many cases however this is already a big help However other extensions do exist for R
76. nt in the construction of the RayTraceFunction source code and only a tiny fraction of the time was actually spent on the ray trace In particular as the number of rays used in a trace is increased the calculation time of TurboPlot relative to AnalyzeSystem improves In addition the trace speed of Turbo Plot depends on the option settings used in the trace For some settings of TurboPlot the actual ray tracing speed can be as much as 30 times faster than AnalyzeSystem This speed improvement with TurboPlot becomes particularly clear when you run multiple traces of the same system because TurboPlot can reuse the RayTraceFunction source code from a previous calculation since this code is passed in the trace output For example what if we wished to observe how the trace appears for different lens focal lengths With TurboP1lot we can introduce a symbolic parameter f that represents the lens focal length and then rerun the trace with different settings for This is accomplished by including both a symbolic and a numeric setting 100 for the focal length parameter in PlanoConvexLens as follows 1994 2005 Optica Software All rights reserved 34 Rayica User Guide In 6 fsystem GaussianBeam 10 1 NumberOfRays gt 11 FullForm gt True Move PlanoConvexLens f 100 50 10 50 Move Screen 50 150 When we call TurboP1lot the first time the result is the same as before In 7 Timing trace TurboPlot fsystem PlotT
77. o Plot on the same system We can use the Timing function to measure the length of time for an activity to occur in Mathematica 1994 2005 Optica Software All rights reserved Rayica User Guide 33 In 23 Timing AnalyzeSystem system AnalyzeSystem GaussianBeam 10 0 1 FullForm gt True NumberOfRays gt 11 Move PlanoConvexLens 100 50 10 50 Move Screen 50 150 Out 23 40 5167 Second 363 ray surface intersections In this ray trace it is evident that the GaussianBeam with FullForm gt True has produced a rectangular shaped array of rays Nevertheless although it is not apparent from the rendering the transverse intensity and optical phase profile of the traced rays have the radial symmetry of an actual Gaussian laser beam Now we will use TurboP1lot on the same system In 15 Timing TurboPlot system Out 15 10 7833 Second traced system Although the overall trace time depends on the particular computer in use the author s computer is particularly slow by today s standards the timing ratio from two different traces will remain fairly constant for different computer systems but perhaps not for different Mathematica versions In the previous example we can see that TurboP1ot in its default setting is about four times faster than AnalyzeSystem Although this speed increase is useful it is still not particularly dramatic However with TurboPlot most of this time was actually spe
78. old 1 GRANT OF LICENSE This Agreement grants you certain limited non exclusive rights iCyt reserves all rights not expressly granted to you 2 COPYRIGHT All rights title and copyrights in and to the SOFTWARE PRODUCT including but not limited to any images photographs animations video audio music text and applets incorporated into the SOFTWARE PRODUCT and any copies of the SOFTWARE PRODUCT are owned by iCyt or its affiliates The SOFTWARE PRODUCT is protected by copyright laws and international treaty provisions Therefore you must treat the SOFTWARE PROD UCT like any other copyrighted material except that you may make one copy of the SOFTWARE PRODUCT solely for backup or archival purposes If the SOFTWARE PRODUCT has been purchased by a legal entity other than an Individual you are entitled to make one copy of the SOFTWARE PRODUCT for home use You may not copy the printed materials accompanying the SOFTWARE PRODUCT 3 PRERELEASE CODE The SOFTWARE PRODUCT may contain PRERELEASE CODE that is not at the level of performance and compatibil ity of the final generally available product offering These portions of the SOFTWARE PRODUCT may not oper ate correctly and may be substantially modified prior to first commercial shipment iCyt is not obligated to make this or any later version of the SOFTWARE PRODUCT commercially available 1994 2005 Optica Software All rights reserved Rayica User Guide 67 4 DE
79. onent or the position of a component or light source in space You can include equations with your symbols or even assign a symbolic wavelength to a light source and subsequently optimize the system at different colors 16 ReadRays with TurboTrace and TurboPlot As shown previously with ReadRays and AnalyzeSystem in Section 12 it is often desirable to get specific parameter values for a selected group of intersection points at an optical surface ReadRays also offers such functionality for Turbo Trace and TurboP1ot calculations by calling ReadTurboRays internally ReadTurboRays results rayparameters selectionproperties takes ray traced results from TurboPlot TurboTrace and returns a list of values for rayparameters and selectionproperties given However the selectionproperties parameter is optional and can be omitted Consequently you either call ReadRays or ReadTurboRays without any change in behavior As a demonstration we will use the plot result from the previous section to examine the optical path length of rays at the screen surface For this we will use the OpticalLength as the rayparameter together with ComponentNumber gt 2 as the selectionproperty in ReadRays In 6 ReadRays plot OpticalLength ComponentNumber gt 2 Outf 6j 155 274 155 243 155 232 155 231 155 232 155 232 155 232 155 231 155 232 155 243 155 274 In 6 ReadTurboRays plot OpticalLength ComponentNumber gt 2 Outf 6j 155
80. only the reflective characteristic of the mirror but also the amount of rotation imposed on the mirror surface 1994 2005 Optica Software All rights reserved Rayica User Guide 61 In 9 AnalyzeSysten LineOfRays 45 NumberOfRays gt 11 TransferTraits Move mirror 0 4 lens 2 Boundary 150 PlotType gt TopView If the donor component contains more than one surface then only the traits from a single surface specified by the DonorSur faceNumber option will be used In general the surfacenumbers parameter of TransferTraits can pass either a list of integers First Last or All as a setting TransferTraits uses the options TransferSurfaceFunction TransferDe flectionFunction TransferRendering and DonorSurfaceNumber 1994 2005 Optica Software All rights reserved 62 Rayica User Guide TransferTraits works equally well with both AnalyzeSystem and TurboPlot ray trace functions Here is an example using TurboPlot This time however we will make the lens a donor and transfer its shape characteristics to the mirror by using the TransferSurfaceFunction gt True option setting This time however we will use TransferDeflection Function gt False in order to not transfer the optical properties of the lens keeping the mirror reflective In 15 TurboPlot LineOfRays 45 NumberOfRays gt 11 TransferTraits lens mirror 1 TransferSurfaceFunction gt
81. or CreateClones Because no z coordinate is given the resulting system will automatically use z 0 and bi sect the x y plane However you can also position your cloned elements in three dimensions if you pass three dimensional coordinates to CreateClones To generate a list of coordinates we will use the Table function of Mathematica In addition we will add a random perturbation to the coordinates with Mathematica s built in Random function In 6 positions Apply Join Table Random Real 25 25 x Random Real 25 25 y x 10 10 1 y 10 10 1 1 Next we use the List Plot function of Mathematica to examine the spatial distribution of coordinate points In 7 ListPlot positions AspectRatio gt 1 1994 2005 Optica Software All rights reserved Rayica User Guide 37 We will now use CreateClones together with TurboP1lot to trace rays through a randomized array of spherical glass ball lenses In order to model a ball lens in Rayica we will use the BallLens component function BallLens diameter options denotes an entire spherical refractive component Finally we trace the system with TurboPlot Here we use CreateClones gt positions to specify the spatial positions of the cloned lenses and the LineOfRays function to generate the rays in the system In 8 TurboPlot Move LineOfRays 20 NumberOfRays gt 21 12 BallLens 6 CreateClones gt positions ShowClones gt True PlotType gt
82. ourceTransformation gt 0 0 0 1 0 0 0 1 0 0 0 1 SourceLevel gt 1 1 NumberOfRays gt 1 BirthPoint gt 0 0 0 CoordinateSystem gt CartesianCoordinates StartAtBirthPoint gt True MonteCarlo gt False SourceID gt 576 SourceFraction gt 1 SourceOffset gt 0 GridSpacing gt 1 amp Because the Source object is automatically created by all of the built in light source functions the user of Rayica never has to worry about the contents of this object In fact unless you use InputForm as demonstrated here you will never even see the contents of another Source object again after this discussion Nevertheless it is helpful to understand what happens when you evaluate a light source function ie it creates a Source object This information is used later by Rayica for ray tracing In the previous result the SingleRay returned to the screen merely identified the type of function that generated the Source object namely by SingleRay In advanced forms of Rayica this self echoing feature enables Rayica to support GUI mouse gestures in addition to the textual entry of optics For the basic Rayica operation discussed here however we will only consider the textual entry of optics A Source object is not directly used for the ray trace calculation Rather the Source information is only used at the start of the ray trace to initiate the rays for the trace Essentially the Source object infor
83. ously conducted by AnalyzeSystem PropagateSystem and Turbo Plot TurboTrace The last five functions OptimizeSystem FindFocus FindIntensity ModulationTransfer Function and TransferTraits are the highest level functions of all and perform very specific tasks as indicated by their given names Rayica offers four simple command tools that provide an overview of the functions used in the Rayica package SourceFunc tions ComponentFunctions MoveFunctions and RayicaFunctions These four commands create a list of the available light sources optical components move functions and available optical functions respectively For example at any time that you wish while working with Rayica you can access a listing of Rayica s primary high level functions with the RayicaFunctions command 1994 2005 Optica Software All rights reserved Rayica User Guide 9 In 7 RayicaFunctions AddSurfaceRoughness Fresnel ReadRays AnalyzeSystem Hole Resonate ConstructMeritFunction ModulationTransferFunction SearchData DataToRayica Move ShowSystem FindFocus MoveSurface TransferTraits FindIntensity OptimizeSystem TurboPlot FindSpotSize ReadData TurboTrace In Mathmatica RayicaFunctions gives you hyperlinks to Rayica s most important high level functions Clicking on any name will give you a description of its use Further each of these lists is hyperlinked to the definitions of the different items contained in them All you
84. play of the system ReadRays results rayparameters selectionproperties takes ray traced results from AnalyzeSystem PropagateSystem as well as TurboPlot TurboTrace and returns a list of values for rayparameters given FindFocus system options determines the minimum spot size for a locus of rays at the last reported surface in the system and plots the results FindSpotSize objectset options determines the spot size for a locus of rays at the last reported surface in the system and plots the results FindIntensity system options calculates the intensity function for each optical surface that gets reported from the ray trace of the system ModulationTransferFunction intensitydata options calculates the modulation and phase transfer functions of an optical system for a given object source input Rayica s ray trace diagnostic functions In addition to the diagnostic functions listed in the above box you can also reuse the ray trace functions AnalyzeSystem and TurboPlot to make different visualizations of previously ray traced information There are also two other important high level functions OptimizeSystem and FindIntensity that take an untraced optical system and perform their own internal ray trace calculations Many examples of these different functions are presented throughout the Rayica documenta tion In the next section we will examine the ShowSystem function and use it to rerender the previous trace result 6
85. r it is always more advantageous to use TurboPlot and TurboTrace when large numbers of rays or iterative processes are required We will now consider AnalyzeSystem in more detail When no light sources are included AnalyzeSystem simply renders the optical components present Here we use AnalyzeSystem to render a plano convex lens In 20 AnalyzeSystem PlanoConvexLens 100 50 10 Axes gt True AnalyzeSystem PlanoConvexLens 100 50 10 Out 20 rendered element 1994 2005 Optica Software All rights reserved Rayica User Guide 19 Here PlanoConvexLens is created with its first surface at the origin and its second surface positioned down the positive x axis In general the aperture parameter of PlanoConvexLens may designate a circle rectangle or polygon depending on the number and type of elements listed by it Here we created a circular lens that has a diameter of 50 millimeters by using 50 in the aperture parameter After rendering the plano convex lens AnalyzeSystem first echoes back the input expres sion and then returns the actual information hidden within the rendered element expression Shortly in Section 7 we will use AnalyzeSystem for ray tracing as well as rendering but first we must learn how to position optical components and light sources in three dimensional space 4 The Move Function To put an optical element at a location other than x 0 y 0 and z 0 you will need to use one of Ray
86. race Sketch gt SurfaceRendering gt Trace EdgeRendering gt Empty CrossRendering gt Fill Trace Wire gt SurfaceRendering gt Mesh EdgeRendering gt Mesh CrossRendering gt Fill Trace Solid gt SurfaceRendering gt Fill Trace EdgeRendering gt Fill CrossRendering gt Empty Notice the option ComponentMedium gt BK7 This option indicates that the refractive material of the planoconvex lens is assumed to be made of BK7 glass material Here the BK7 symbol specifies a particular wavelength dependent model for the refractive index However you can also specify a fixed numeric value for ComponentMedium as shown below In this case the refractive index is held constant for all wavelength values In 19 PlanoConvexLens 100 50 10 ComponentMedium gt 1 5 Out 19J PlanoConvexLens 100 50 10 ComponentMedium gt 1 5 1994 2005 Optica Software All rights reserved 18 Rayica User Guide 3 Introduction to AnalyzeSystem and TurboPlot Rayica has two parallel methods for doing ray tracing and rendering of optical systems One method uses the AnalyzeSys tem function originally known as DrawSystem while the second method uses the TurboPlot function Each method offers similar functionally in a parallel way AnalyzeSystem is good for generating illustrations for publication and tracing small numbers of rays while TurboP1lot is best for working with large numbers of rays After making so
87. re is a description of FindFocus FindFocus objectset options determines the minimum spot size for a locus of rays at the last reported surface in the system and plots the results Next we can use the FindFocus function to find focal point of our lens system In this case since we have already calcu lated a ray trace using TurboP1lot we can simply pass to FindFocus the result of our previous calculation In 44 focus FindFocus trace 0 05 0 05 f 0 1 0 05 0 0 05 0 1 Out 44 Screen gt Move Screen 0 231204 218 522 TurboSystem gt traced system FocalPoint gt 218 522 0 0 FocusType gt RMSFocus WeightedSpotSize gt 0 0170665 SpotSize gt 0 0264831 BackFocalLength gt 158 522 FocalPlaneTilt gt 1 0 0 TurboRays gt ray intercepts of 1 surfaces FindFocus has automatically generated a plot of the locus of rays at the focal plane In addition FindFocus returns a series of rules that describe various aspects of its focus calculation You can learn more about FindFocus in Section 1 3 5 of the Principles of Rayica discussion Of the different rules returned by FindFocus we are only presently interested in the FocalPoint rule since it holds the three dimensional focal point coordinates As such we can assign the focal point result to a focalpoint variable in the following way In 45 focalpoint FocalPoint focus Out 45 218 522 0 0 1994 2005 Optica Sof
88. res not covered in the basic package 63 Features left to the future 63 22 Backward Compatibility Issues 64 Single User License Agreement 66 Contact Us Optica Software Division of iCyt Mission Technology 2100 South Oak St Champaign IL 61820 USA voice 1 866 328 4298 fax 217 328 9692 support opticasoftware com 1994 2005 Optica Software All rights reserved Rayica User Guide 3 1 Introduction Nearly every optical engineering endeavor can benefit from the use of Rayica including but not limited to optimization lasers and resonators non sequential calculations stray light analysis time dependent optical systems imaging systems spectroscopic measurement astronomical systems solar concentrators fiber optic systems opto mechanical systems polarization calculations turbulent media and photon density calculations This guide will get you acquainted with Rayica s most important features By learning the functions introduced here you will have a good foothold for using Rayica In particular you will learn how to model optical components and light sources together for ray tracing as well as receive an overview of Rayica s most important capabilities In addition to this User Guide advanced information is provided in the companion Principles Of Rayica guide as well as through our website www opticasoftware com Before beginning however you must first load Rayica into memory Loading Rayica The basic Rayica packag
89. riety of input formats used with Move These are shown below Move objectset x y rotationangle Move objectset x rotationangle Move objectset x Move objectset x y Move objectset x y Z Move objectset x y Z axisvector Move objectset x y Z axisvector twistangle Move objectset x y Z rotationmatrix Common input formats for Move Although not shown these formats all accept options Including the Move function Rayica has eight positioning directives At any time that you wish while working with Rayica you can access a listing of Rayica s positioning functions with the MoveFunctions command In 10 MoveFunctions Move MoveDirected MoveReflected Rotate MoveAligned MoveLinear MoveSurface Translate In Mathmatica MoveFunctions gives you hyperlinks to Rayica s most important positioning functions Clicking on any name will give you a description of its use You can learn more about how to use Move and the other directives in Chapter 2 the Placement Directives chapter of the Principles of Rayica discussion 5 Using AnalyzeSystem for Ray Tracing Tracing a single ray We are almost ready to use AnalyzeSystem for ray tracing First however we need to consider a boundary to contain the rays Otherwise the traced rays will terminate on the last surface of the last optical component in the system The easiest way to define a boundary is with the Boundary
90. s at the focal plane Using the optical path length parameter OpticalLength you can use the ComponentNumber gt 3 as a selection property to examine the optical path length from the ray starting point to the surface of the screen component 1994 2005 Optica Software All rights reserved Rayica User Guide 31 In 33 ReadRays screensystem OpticalLength ComponentNumber gt 3 Out 33 228 591 228 435 228 369 228 538 228 538 228 369 228 435 To see more decimal places you can use InputForm In 34 InputForm Out 34 InputForm 228 591359124603 228 43455070396408 228 3688128926051 228 53755280486945 228 53755280486945 228 36881289260504 228 43455070396408 Note that addition to working with AnalyzeSystem PropagateSystem ReadRays can also employed with results from TurboPlot TurboTrace In such instances however ReadRays makes an internal call to ReadTurboRays for its results ReadTurboRays is discussed further in Section 16 13 The PropagateSystem Function PropagateSystem is called internally by AnalyzeSystem to perform its ray trace calculations Here we define Propagate System PropagateSystem objectset options takes objectset made up of a mixed list of Source Component and OpticalSystem objects traces the rays through the components and returns the ray tracing result as an OpticalSystem object carrying the final ray trace information Since PropagateSystem performs r
91. s been no mention about the modelling of optical coatings polarized elements polarization ray tracing bi refringence diffraction gratings custom ized optical elements or user defined surface shapes Nevertheless all of these capabilities are a part of the basic Rayica package and is documented further in the companion Principles Of Rayica guide as well as through our website www opticasoftware com The basic package also includes special functions for importing data from other ray trace packages such as Zemax and Code V Using Mathematica s Import function you can also import and export some data formats between mechanical CAD packages and Rayica You can also build new refractive material models and create your own new deflection models with the same mechanisms that enable Rayica to model refraction reflection and diffraction on optical surfaces You can model new optical components from scratch with the generic building block language used by Rayica to model its built in component functions There is also a built in facility to model bulk material effects such as gain and absorption as well as user created bulk material behaviors such as photon diffusion and graded index refraction The Rayica database is also fully extensible and Rayica provides special functions to help you add your own database items Unfortunately the complete coverage of the every aspect of Rayica s capabilities is simply too vast to mention within a single introductory dis
92. system you have created you can access a list of available functions using the RayicaFunctions command Basic Steps to follow when creating an optical system 1 Determine what light source to use 2 Create a component list see the Resonate section if you have any composite lenses 3 Position the components in your list using the Move function 4 Bound the system using a Screen or a Boundary 5 Assign the resulting system to a variable 6 Use different high level functions to analyze the system as necessary Variable definition It is an excellent idea to assign the system to a variable as shown below In 14 opticalsystem LineOfRays 45 NumberOfRays gt 11 Move PlanoConvexLens 100 50 10 50 Move Screen 50 200 Out 14J LineOfRays 45 NumberOfRays gt 11 Move PlanoConvexLens 100 50 10 50 Move Screen 50 200 When an optical system is assigned to a variable you can then use that variable to perform any number of calculations It is always a good idea to assign an optical system to a variable if you intend to use the same system for repeated calculations as this can dramatically reduce input time What is further you can assign the output of a function to a variable as shown below 1994 2005 Optica Software All rights reserved 6 Rayica User Guide In 16 tracedresult TurboPlot opticalsystem VEA ON A lt y ez ei ZAR Saw N DS S a AY am
93. t the SOFTWARE PRODUCT will detect all viruses Trojan horses worms or other software routines or hardware components designed to permit unauthorized access to or to disable erase or otherwise harm any software hardware or data iCyt s entire liability and your exclusive remedy shall be repair or replacement of any SOFTWARE PRODUCT that does not meet the foregoing warranty when returned to iCyt This limited warranty is void if failure of the SOFT WARE PRODUCT has resulted from accident abuse or misapplication Any replacement software will be war ranted for the remainder of the original warranty period or thirty 30 days whichever is longer THE FOREGOING EXPRESS LIMITED WARRANTIES ARE IN LIEU OF AND TO THE MAXIMUM EXTENT PERMIT TED BY APPLICABLE LAW ICYT SPECIFICALLY DISCLAIMS ANY AND ALL OTHER WARRANTIES EXPRESS OR IMPLIED INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE WITH REGARD TO THE SOFTWARE PRODUCT 1994 2005 Optica Software All rights reserved Rayica User Guide 69 TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW IN NO EVENT WILL ICYT OR ITS DISTRIBUTORS OR DEALERS BE LIABLE FOR SPECIAL INCIDENTAL INDIRECT OR CONSEQUENTIAL DAMAGES WHATSOEVER INCLUDING WITHOUT LIMITATION DAMAGES FOR LOSS OF INCOME PROFITS USE OF INFORMATION OR ANY OTHER PECUNIARY LOSS ARISING OUT OF OR IN CONNECTION WITH THE SOFTWARE PRODUCT EVEN IF ICYT HAS BEEN ADVISED OF THE POS
94. te order that is more intuitive In particular Function s Gx s t Gy s t Gz s t for grating functions and Gx Gy Gy for constant grating vectors are now used instead of Function s t Gy s t Gz s t Gx s t and Gy Gz Gx If you are interested to recover the original Grating behaviors of Optica you can call SetOptions with Grating as shown SetOptions Grating RayicaVersion gt 1 1994 2005 Optica Software All rights reserved 66 Rayica User Guide SINGLE USER LICENSE AGREEMENT FOR LENS LAB RAYICA and WAVICA SOFTWARE PRODUCTS IMPORTANT READ CAREFULLY This Single User License Agreement Agreement is a legal agreement between you a single person or entity and the Optica Software Division of iCyt Mission Technology Inc i Cyt an Illinois corporation for one or more of the software products identified above which includes computer software and online or electronic documentation and may include associated media and printed materials SOFT WARE PRODUCT or SOFTWARE By installing copying or otherwise using the SOFTWARE PRODUCT you agree to be bound by the terms of this Agreement If you do not agree to the terms of this Agreement do not install or use the SOFTWARE PRODUCT SOFTWARE PRODUCT LICENSE The SOFTWARE PRODUCT is protected by copyright laws and international copyright treaties as well as other intellectual property laws and treaties The SOFTWARE PRODUCT is licensed not s
95. the initial example will be discussed in specific with references to later sections of this booklet for more extensive explanations of the functions used In 13 TurboPlot LineOfRays 45 NumberOfRays gt 11 Move PlanoConvexLens 100 50 10 50 Move Screen 50 200 Out 13 traced system Inputting data The first thing about this example to observe is the format Because Rayica uses a text based input system it does not matter whether or not you include line breaks where they have been included They have been put into this example for the sake of clarity The generated image can be instantly resized by selecting a corner of the image and dragging the corner of the picture until in is the desired size Another important note about entering data in Rayica is that every function in Rayica has a specific input format For exam ple the input format for TurboPlot is TurboPlot system options TurboPlot takes two different inputs an optical system system and any option definitions options When any input variable contains multiple elements in this case an optical system it is necessary to enclose those elements in curly brackets As with any mathematical system it is important to close all brackets and parentheses appropriately or else the calculation will fail Note that sometimes an input element is not required for final calculation TurboPlot does not require that options be entered in order to perform a cal
96. tion 3 6 3 of the Principles of Rayica Guide However since this is not the main focus of the basic Rayica package in general such efforts will be left to Wavica Instead most of the topics and examples given in this User s Guide will concentrate on the use of Rayica for endeavors that involve geometric ray trace calculations In addition to Wavica there are several other extensions for Rayica either being planned or presently developed At the time of this writing there are three additional extensions to Rayica under consideration These are global optimization distributed ray tracing on networked computer systems and a laser design package 1994 2005 Optica Software All rights reserved 64 Rayica User Guide Features left to the future Until now all parts of Rayica and its extensions have utilized ray trace calculations for some aspect of its package function Unfortunately this has left out some important optical design tools which for example depend heavily on coupled wave theory or finite element analysis Such applications include thin film design and integrated optics optical waveguides Until now we simply haven t had the time and resources to development these important tools In general we always welcome possible collaborations with scientists and engineers that could lead to such applications in Mathematica Finally some of Rayica s present limitations are due to the current state of Mathematica In particular
97. to TurboPlot a new light source function as the first parameter and the previous trace result as the second parameter Here we swap the Gaussian Beam source with a LineOfRays source as well as change the focal length value to gt 90 In 64 Timing TurboPlot LineOfRays 30 NumberOfRays gt 100 trace SymbolicValues gt gt 90 PlotType gt TopView Out 64 3 71667 Second traced system In addition to shorter computation times TurboPlot consumes far less memory than AnalyzeSystem In particular the traced ray information is stored much more efficiently by an order of magnitude in some cases with TurboP1lot Until now the performance gains of TurboPlot have been an order of magnitude better than AnalyzeSystem Next we will introduce the CreateClones option for modeling repetitive optical elements In particular with this option we can obtain performance gains in terms of both speed and memory that are three orders in magnitude better than AnalyzeSystem 1994 2005 Optica Software All rights reserved 36 Rayica User Guide CreateClones With TurboPlot TurboTrace Rayica now has an enhanced capability for model
98. tted in the same fashion In order to get an item from the database you must specify one or more of the properties that you require In this example we had specified OpticalMedium gt BK7 to recover the database entry for BK7 glass When you first begin to use Rayica s database you will need to have some idea of the information that you are searching for In particular you must decide whether you are searching for a particular type of optical component or optical glass for example The problem is that Rayica s database can contain many different types of information for each database entry In order to gain a listing of all database parameternames that are available you can call SearchData without specification 1994 2005 Optica Software All rights reserved Rayica User Guide 55 In 69 SearchData Out 69J A AcidResistance AlkaliResistance AngleTolerance BackFocalLength Baffled BubbleClass CatalogFocalLength CatalogNumber Centered CenterThickness ClearAperture ClimaticResistance ColorCode CompanyAddress CompanyName ComponentBoundary ComponentLabel ComponentMedium Country CurvatureTolerance D DataComments DataSource Date DefaultAngleSetting DesignRefractivelIndex DesignWaveLength DiffractionLimitedRange DimensionalTolerance Dispersion EdgeThickness ElasticModulus EntrancePupilDiameter EquivalentMagnification EvenFunction FaxNumber FieldOfView FieldStopLocation FileName FlatSubstrate FN
99. tware All rights reserved Rayica User Guide 45 Measuring the Point Spread Function We are now ready to apply FindIntensity to our lens system to measure the point spread function of the system This time we will place a Screen object at the focalpoint determined by FindFocus In 47 focusintensity FindIntensity GaussianBeam 5 05 NumberOfRays gt 32 FullForm gt True Move ApertureStop 50 15 49 Move PlanoConvexLens 100 50 10 50 Move Screen 6 6 focalpoint Plot2D gt False Surface Information ComponentNumber gt 3 SurfaceNumber gt 1 NumberOfRays gt 956 SmoothKernelSize gt 0 020986 Surface Intensity Out 47 ComponentNumber gt 3 Energy gt 99 257 Full3D gt True IntensityFunction gt CompiledFunction intensity data NumberOfRays gt 956 OutputGraphics gt SurfaceGraphics RayBoundary gt 0 0524651 0 0524651 0 0524651 0 0524651 SmoothKernelSize gt 0 020986 SurfaceNumber gt 1 WaveFrontID gt 1 Previously we had used Plot2D gt False to display a three dimensional plot of the surface intensity profile Next we will call FindIntensity for a second time with Plot2D gt True to examine the intensity function along the horizontal axis of each surface In 48 FindIntensity focusintensity Plot2D gt True Surface Information ComponentNumber gt 3 SurfaceNumber gt 1 NumberOfRays gt 956 SmoothKernelSize gt 0 020986 Sur
100. u can change the way a component function is rendered with the GraphicDesign option GraphicDesign gt style is an option of all rendered components the designates the style of rendering GraphicDesign can be set to a number of different style settings These include Automatic Sketch Wire Solid or Off False In most cases GraphicDesign is used by component functions and is not passed directly to high level render ing functions such as ShowSystem or AnalyzeSystem Here we use GraphicDesign gt Wire with PlanoConvexLens and GraphicDesign gt Off with Boundary In 6 AnalyzeSystem ConeOfRays 20 NumberOfRays gt 7 Move PlanoConvexLens 100 50 10 GraphicDesign gt Wire 100 Boundary 0 25 25 200 25 25 GraphicDesign gt Off Now we use PlotType gt SideView with ShowSystem to look at the rendered result from the side In 21 ShowSystem PlotType gt SideView Wwryyyyy The symbol feeds the output from the previous result into the expression input In this example the output from Analyze System of the last example has been used as input to ShowSystem You can also view the result from the front with Plot Type gt FrontView 1994 2005 Optica Software All rights reserved 26 Rayica User Guide In 22 ShowSystem PlotType gt FrontView 8 Adding a Cylindrical Lens to the System For some additional interest you can pla
101. uide 19 Rayica s Database Rayica now supports a database system that contains information on a wide variety of optical materials and components These items represent the manufactured products of many different companies This information is initially stored on the computer s hard disk but once loaded the entire database contents is held in the computer s memory Rayica s database is not initially loaded into the computer s memory until it is accessed for the first time After this point all of the database contents stay in the computer s memory for the remaining duration of the Mathematica session Rayica has a suite of functions for managing the database information The most important are DataToRayica SearchData and ReadData For the full listing of database related functions see Section 5 2 of the Principles of Rayica Guide DataToRayica selectionproperties options is used to build models in Rayica of optical components light sources coatings and materials from the information given in databaselist DataToRayica first calls SearchData to select for specific data items SearchData selectionproperties options uses the internally loaded catalog database to give a selected listing of catalog entries ReadData parameters selectionproperties options uses the internally loaded database to give a selected listing of the specified data related parameters Of these three functions DataToRayica operates at the highest
102. umber FocalLength FrontFocalLength FullForm GlassCatalogs GlassCodeNumber Hole HousingBoundary IndexCoefficients InputEdgeThickness InternalTransmittance KnoopHardness Magnification MassDensity MeltingPoint Mirrored ModeliIntensity NA NumberElements NumberOfElementGroups NumberOfSurfaces OffAxis OpticaFunction OpticalMedium PhosphateResistance PoissonRatio PrinciplePointSeparation RadiusOfCurvature ReferenceWaveLengthNumber Reflectance RefractiveIndex SAY ScratchDig Solubility SpecificHeat SpectralIndex SplitRays StainResistance StopPosition SurfaceAccuracy SurfaceBoundary SurfaceCoating SurfaceCurvature SurfaceFunction SurfaceLabel SurfaceSeparation SurfaceShape SurfaceValue TelephoneNumber TemperatureCoefficientIndex ThermalConductivity ThermalExpansion ThicknessTolerance TransformationTemperature TransmissionRange Transmittance Units V1H1 V2H2 ViscousTemperaturel ViscousTemperature2 WaveFrontFlatness WaveLengthRange WebSiteAddress WindowParameters WorkingDistance Of these many parameternames only a few are really useful for conducting searches The most useful parameternames include CatalogNumber ComponentBoundary CompanyName FocalLength RayicaFunction and OpticalMedium These are defined below CatalogNumber gt string specifies the catalog identification number for a component ComponentBoundary gt boundary specifies the entrance dimensions for a lens and the overall dim
103. urfaces Next use RayChoice gt ComponentNumber gt 2 with PlotType gt Surface to view the intersection points on the two surfaces of the cylindrical lens In 28 ShowSystem opticalsystem PlotType gt Surface RayChoice gt ComponentNumber gt 2 1994 2005 Optica Software All rights reserved Rayica User Guide 29 10 Using Screen to Look at the Focal Plane The Screen component function models a single surface that samples rays at a given plane in space You can use Screen to look at the focal plane of a system or to get the planar cross section of ray information anywhere in the system More advanced screens can have curved surfaces and circular or polygonal boundaries Here is the definition of Screen Screen aperture options denotes a planar component that intersects rays without disturbing them Next we use Screen with AnalyzeSystem to inspect the focal plane of the optical system from Section 9 Here we use Move to place the screen at the focal position x 218 as measured previously In 29 screensystem AnalyzeSystem ConeOfRays 20 NumberOfRays gt 7 Move PlanoConvexLens 100 50 10 100 Move PlanoConvexCylindricalLens 100 50 50 10 130 Move Screen 50 50 218 Boundary 100 100 100 250 200 200 GraphicDesign gt False By using PlotType gt Surface with RayChoice gt ComponentNumber gt 3 you can clearly see ray intersection points at
104. ustomPrism ParabolicLensSurface Solitaire CustomScreen ParabolicMirror SphereGraphic CylinderGraphic PechanPrism SphericalBaffle CylindricalBaffle PellinBrocaPrism SphericalBeamSplitter CylindricalLens PentaPrism SphericalDiffuser CylindricalLensSurface PinHole SphericalDiffuserMirror CylindricalMirror Pipe SphericalGratingMirror BiConcaveLens CylindricalScreen PlanoConcaveCylindricalLens SphericalLens BiConvexCylindricalLens Diffuser PlanoConcaveLens SphericalLensSurface BiConvexLens DiffuserMirror PlanoConvexCylindricalLens SphericalMirror BirefringentLensSurface DirectVisionPrism PlanoConvexLens SphericalScreen Boundary DovePrism PolarizingBeamSplitterCube SquareConeMirror Box DTIRCLens PolarizingPrism SurfaceFacet BoxGraphic DTIRCLensSurface PolygonalMirror ThickLens CircleGraphic Fiber PolygonGraphic ThinLens ClearBoundary FresnelRhomb PorroPrism ToroidalLens CompoundLens FunnelLens Prism ToroidalLensSurface ConjugateMirror FunnelLensSurface RectangleGraphic ToroidalMirror CustomBaffle Grating RetardationPlate WedgePrism CustomBeamSplitter GratingMirror ReversionPrism Window CustomBirefringentLensSurface HalfBallLens RhomboidPrism WinstonConeMirror CustomConjugateMirror HollowCornerCube RodBaffle CustomDiffuser JonesMatrixOptic RodLens In Mathmatica ComponentFunctions gives you hyperlinks to Rayica s current component functions Clicking on any name will give you a description
105. w N Out 16J traced system Basic commands If you already know the name of command that you want to include in your optical system but would like to review the definition before actually including it you can use the command to display the definition In 11 PlanoConvexLens PlanoConvexLens focallength aperture thickness label options denotes a lens with a planar surface on one side and a convex spherical surface on the other side PlanoConvexLens is created with its first surface centered about the origin and its second surface positioned down the positive x axis The aperture parameter may designate a circle rectangle or polygon depending on the number and type of elements listed by it The user named label parameter is optional and can be omitted When it is present its text content is used to identify the object in both the rendered graphics and the output cell expression When it is omitted Rayica uses the default setting of the Labels option with the rendered graphics Note that the specified focallength is always determined for a particular setting of the DesignWaveLength and ComponentMedium options By default Rayica uses DesignWaveLength gt 0 5461 microns and ComponentMedium gt BK7 Care should be taken to insure that these default settings are compatible with the intended experimental design or unintended results can occur The command works with all defined elements of Rayica from functions to li
106. y use it in a ray trace calculation Here is how you evaluate the SingleRay function and assign its information to a variable called lightsource 1994 2005 Optica Software All rights reserved Rayica User Guide 11 In 16 lightsource SingleRay Out 16J SingleRay Rayica normally hides the contents of its light sources by echoing the function input back to the screen For a first time user of Rayica this can be a bit disconcerting since it appears that nothing has occurred at all For this reason Rayica changes the returned text color typically to green for valid entries instead of using the default black color of ordinary Mathematica output This color change indicates that the input has been correctly evaluated by Rayica If there is no color change then the function has not been recognized by Rayica and most likely there has been a typographical mistake In addition if you use InputForm as shown below you can see that the SingleRay function has actually generated a hidden packet of informa tion that is encapsulated by a Source object In 3 lightsource InputForm Out 3 InputForm Source SourceDescription gt SourceDescription SingleRay Ray 1 SourceTransformation gt 0 0 O 1 0 0 0 1 0 0 O 1 SymbolicSourceTransformation gt 0 0 0 1 0 0 0 1 0 0 0 1 SourceTransformation gt 0 0 0 1 0 0 0 1 0 0 0 1 SymbolicS
107. ype gt TopView Out 7J 10 4833 Second traced system After this trace has occurred once we can then rerender the ray trace information much more quickly by passing trace back to TurboPlot In 8 Timing TurboPlot trace Out 8 1 38333 Second traced system Because we have not changed any parameters TurboPlot has simply rerendered the previous calculation without rerunning the trace In this instance TurboPlot takes the role of ShowSystem discussed previously in Section 7 However we can also run a new ray trace with different symbolic parameter values at much greater speed In order to accomplish this we use the SymbolicValues option 1994 2005 Optica Software All rights reserved Rayica User Guide 35 Symbolicvalues gt symbol gt value is an option that attaches numerical values to the specified symbolic variable names Next we will change the value for the lens focal length from 100 to 75 In 54 Timing TurboPlot trace SymbolicValues gt f gt 75 PlotType gt TopView Out 54 4 58333 Second traced system This time the overall trace and rendering time is 10 times shorter than AnalyzeSystem could have managed if it indeed accepted symbolic settings In addition to using different symbolic settings TurboPlot also accepts new light sources on the fly without having to recompile the ray trace information This is accomplished by passing

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